Suppose we were instead asked to calculate the integral x sin(x) dx. Can you calculate this integral using the method of substitution?

Q: Find the indefinite integral.

A: To Find the indefinite integral. Substitution  u = x3 du = 3x2 dx du/3 = x2 dx

Q: Find the indefinite integral using the substitution x = 4 sin θ

A: Given :              The indefinite integral                                 ∫x316-x2dx

Q: Use a table of integrals to find the indefinite integral.

A: To find: The integration of ∫e3x1+ex3dx. Formula used: Power rule of integration: ∫xndx=xn+1n+1+C…

Q: What is the integral of dx/((1+x^2)^2)

A: Given integral Now,

Q: Find the indefinite integral using the substitution x = 4 sin θ.

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Q: Evaluate the integrals ∫ex sin (ex) dx

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Q: Consider , xe* dx. What will be the appropriate solution and answer to this improper integral? lim,-…

A: Given definite integral is ∫−∞1xe−x2dx

Q: Find the indefinite integral using the substitution x = 8 sin(@). (Use C for the constant of…

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Q: e3x sin x dx

A: We will integrate this integral using integration by parts twice

Q: x sin¬1 x² dx

A:

Q: Select the basic integration formula you can use to find the indefinite integral, and identify u and…

A: Consider the given integration as

Q: Evaluate the improper integral. If the integral diverges, state so. dx 1. dx 2. (x + 1)² 0.

A: 1.Given, II=∫1∞dxx23As it is an improper integral,we write it as=limt→∞∫1tdxx23=limt→∞∫1tdxx232…

Q: Find the indefinite integral. (Use C for the constant of integration.) sin(a^) « dx

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Q: Evaluate the indefinite integral given below. 2e3 sin (4z) cos (4x) dx Provide your answer below:…

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Q: 00 1 dx x(Inx)2

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Q: 14. [ –3 sin (10x)dx

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Q: xe dx

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Q: Find the indefinite integral. sinh(4 - 7x) dx Step 1 First, let u = 4 - x. Now, differentiate u with…

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Q: dx (apply the properties on how to solve improper integrals 1 – x²

A: Given query is to find the value of the integral.

Q: sin x dx dy, is The value of the integral equal to

A: Direct integration is not possible in this case so here first we switch the order of integration of…

Q: Evaluate the integral. x sin(10x) dx + C

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

A: Consider the given expression as dydx=4x+4x16-x2

Q: Find the indefinite integral. (Use C for the constant of integration. sin 4x sin 3x dx sin x sin 7x…

A: Solution is given in step 2

Q: dx 4ーx2 く

A: Solve improper integral by using partial fraction decomposition

Q: x²+2x+1 dx (x+2)(x−1)²

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Q: Evaluate the integral I sin(x)e-" dx.

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Q: Consider dx. What will be the appropriate solution and answer to this improper integral?

A: Here we have to find the appropriate solution and answer to this improper integral∫-∞1xe-x2dx

Q: Use a table of integrals to evaluate the definite integral.

A: Let the given integral be y - y = ∫012x3ex2dxy = ∫01x2ex22xdxLet,t = x2Differentiating on both sides…

Q: Evaluate the integral.  integral sin 6  x  dx

A: Given ∫sin6x dx We use sin2x=1-cos2x2cos2x=1+cos2x2

Q: 1 |xe*dx 1-

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Q: 4. Calculate the integral, f 4e" sinh x dx.

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Q: '1+ sin x t00 dx x2

A: Given:       ∫π+∞1+sinxx2 dx

Q: Evaluate the integral of (x^2)sin(x^2) dx as an exact answer.

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Q: Evaluate the integrals ∫sin x cos x dx

A: Given: The integration∫sinxcosxdx, To Evaluate: The given indefinite integration.

Q: Find the indefinite integral below and check your work by differentiation: 1 S Væ + -dx

A: Solution: The objective is to find the value of given integral

Q: Evaluate the integral using an appropriate method. T/3 x sin(3x) dx

A: ∫0π3x sin(x)dx

Q: Evaluate the improper integral or show that it diverges. (1+4x)e*dx

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Q: In(sin x) d.x 2

A: We need to find whether given integral is proper of improper.

Q: Find the indefinite integral. (Use c for the constant of integration.) cos° x sin x dx ()30 + 30+

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Q: evaluate the definite integral.

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Q: ,2 x sin x dx

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Q: cos xdx 10. sin x

A: According to definition ∫f(x)dx=F(x), where dFdx=f(x).The function F(x) is called the antiderivative…

Q: dx -> X-VX dx 12 X-(X) b.) =In (x-1x)?

A: Solve the given integral

Q: find the indefinite integral 1十xe dx

A: To find the indefinite integral  integration (6/(1+x²))dx

Q: -dx e2a

A: Given: ∫01xe2xdx

Q: In x dx .2

A: We need to solve the integral.

Q: (xª+1)dx a²(x+1)?

A: Given that a integration we solve it by using general formulas of integration. We know that partial…

Q: 3+ In(2x) dx 00 X-1 1

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Q: Find the integral. e4x sin(6x)dx =

A: To find the integration.

Q: Find the indefinite integral. (Use C for the constant of integration.) sin(2x) cos(2x) dx

A: