Find the indefinite integral and check the result by differentiation. dx 5 - 9x2 Part 1 of 7 (5 - x²). g(x) = (5 – 9x²). Observe that is the derivative of Let Multiply and divide the integrand by and rewrite the integral. 1 -3 5 - 9x2) dx = 9x2) (-18x) dx

Q: Given the integral ( 12x3 + 7 dx -5 Use the integral table to help you find the Anti Derivative of…

A: To evaluate: ∫-5712x3+7 dx We know that  ∫xndx=xn+1n+1, ∫kf(x)dx=k∫f(x)dx and  ∫abf(x)dx=F(b)-F(a),…

Q: In this problem, use properties of definite integrals. 9. Vx2 - x² - 1 dx. Evaluate

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 31 -1 dx 7х — 6 -

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Q: Find the indefinite integral and check the result by differentiation

A: Given: Let I=∫5x 1-x23 dx To Find: To evaluate the given integration and to check the result by…

Q: Find the indefinite integral and check the result by differentiation. 3 3 dx (5 – 9x2

A: Given               ∫x(5-9x2)3 dx

Q: Find the indefinite integral and check the result by differentiation                   ∫x2(6 − x3)5…

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Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: We write the expression using exponent and then integrate C=integrating constant

Q: Find the indefinite integral and check the result by differentiation

A: Given, I=∫x2-932xdx

Q: Find the indefinite integral and check the result by differentiation. dx 9x2 Part 1 of 7 Observe…

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Q: Find the indefinite integral and check the result by differentiation.

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Q: Find the indefinite integral and check the result by differentiation.

A: To find the integral

Q: 3. Use properties of logarithms and/or logarithmic differentiation to find the indicated derivatives…

A: a.)  y =ddxlnx2   ⇒y =2ddxlnx =2x                                                  ln(ab)…

Q: 23. (x + 1)(3x – 2) dx

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Q: Use implicit differentiation to prove that la"] = d nxn-1 dx

A: ddx(xn)=nxn-1

Q: Find the indefinite integral and check the result by differentiation.

A: Given: Let I=∫x21+x32 dx To Find: To evaluate the given integral and to check the result by…

Q: -4t Find the indefinite integral dt and verify the result by differentiation. (t2+3)3

A: Integrate using substitution than take derivative to verify the result.

Q: In the given question verify the statement by showing that the derivative of the right side equals…

A: Consider the given: ∫−6x4dx=2x3+CDerivative of right…

Q: Use chain rule of differentiation to find  Y is equal to 3x²-5x +12 X is equal to 2u²-5u +11 Find…

A: Consider the given function asy=3x2-5x+12 And x=2u2-5u+11

Q: Find the indefinite integral and check the result by differentiation                    ∫ x2(2x3 −…

A: Consider the following integral: ∫x22x3-14dx Substitute 2x3-1=u→6x2dx=du→x2dx=16du in the above…

Q: Find the indefinite integral and check your result by differentiation. (Use C for the const (x³ -…

A: The given integral is ∫x3-12x-4dx use the integration formulas, ∫xndx=xn+1n+1+C∫dx=x+C use the…

Q: Evaluate the definite integral. "1/3 3 dx V1- 9x²

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Q: Find the indefinite integral and check the result by differentiation.

A: Given, I=∫x34+1dx Or  I=∫x34+1dx

Q: Find the indefinite integral and check the result by differentiation.

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Find the indefinite integral and check the result by differentiation

A: Explanation: Given that, ∫x2(6-x3)5dx   Substitute the  u=6-x3du=-3x2dxdx=du-3x2   Now put this…

Q: Find the indefinite integral and check the result by differentiation

A: We have to find out the indefinite integral. ∫tt2+2dt For this integral apply the substitution…

Q: Find the indefinite integral and check the result by differentiation. ∫3√x2 dx

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Q: Find the indefinite integral and check the result by differentiation.                   ∫(x3/2 + 2x…

A: Recall: Integral of xndx = xn+1 / (n + 1)  + C

Q: Find the indefinite integral and check the result by differentiation.

A: ∫7x1-x23dxTake the constant out:  ∫a·fxdx=a·∫fxdx=7·∫x1-x23dxSubs u = 1-x2=7·∫ -12u3duTake the…

Q: Find the indefinite integral and check the result by differentiation                         ∫ 6x2 /…

A: Consider the following integral: ∫6x24x3-93dx Substitute 4x3-9=u→12x2dx=du→6x2dx=12du in the above…

Q: 1-sin 2x dx 2 x-sin x

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Find the indefinite integral and check the result by differentiation.

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Q: Compute the fourth derivative of cos(x+1) - ln(x²+4) + x²²+1 with respect to x. Also, compute the…

A: Sol:- First part:- Fourth Derivative of given function:-…

Q: d Use implicit differentiation to prove that x"| = nx"-1 dx

A: Implicit differentiation is a method to solve the differentiation of an equation without the need to…

Q: 6) S(x + 2)dx

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Q: Find the indefinite integral and check the result by differentiation. ∫(x + 7) dx

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Q: Find the indefinite integral and check the result by differentiation.

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Q: Use the methods of differentials to estimate the value of (x+1) over the square root of 2x+1 at…

A: Use the quotient rule to find the derivative for f(x).

Q: |(4x2 + 3)?dx

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Q: Find the indefinite integral and check the result by differentiation                   ∫(x2 −…

A: Given, I=∫x2-932x dx

Q: Find the indefinite integral and check the result by differentiation                     ∫x3(x4 +…

A: ∫x3x4+32 dx Put, x4+3=t⇒4x3+0=dtdx⇒4x3 dx=dt⇒x3 dx=dt4 Therefore, ∫x3x4+32 dx=∫t2 dt4=14∫t2…

Q: 3. Use Log Rule to integrate. J6x-5 dx a. 6х-5 b. S- 1 dx x Inx

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Q: Find the indefinite integral and check the result by differentiation. COS X 1 - cos²x dx

A: Recall; sin2x+cos2x=1

Q: Find the indefinite integral and check the result by differentiation                     ∫x2 / (1 +…

A: Find the indefinite integral and check the result by differentiation                     ∫x2 / (1 +…

Q: Find the indefinite integral and check the results by differentiation |(4x² + 3)*dx

A: Given integral is∫4x2+32dx. ∫4x2+32dx=∫16x4+24x2+9dx=16x55+24x33+9x+C=16x55+8x3+9x+C

Q: Find the indefinite integral and check the result by differentiation                 ∫5x 3√(1 − x2)…

A: Given integral is ∫5x31-x2dx.

Q: Find y' by direct differentiation (with respect to x). y = (5x2 + 6x − 7) ln x   and  y = (e-x)/…

A: Solution -a.)Given function -y = 5x2+6x-7lnxDifferentiating on both sides with respext to x,dydx =…

Q: 15)S (VA +) dx

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Q: Find the indefinite integral and check the result by differentiation                    ∫x(5x2 + 4)3…

A: The given integral ∫x5x2+43dx can be evaluated as, ∫x5x2+43dx=∫x5x23+35x22×4+35x216+43dx…

Q: -1/16 dx =

A: Integration

Q: Use implicit differentiation to prove that d/dx [ xn ] = nxn − 1

A: Here we use implict differentiating to prove thatddxxn = nxn-1