First make a substitution and then use integration by parts to evaluate the integral. (Use C for the constant of integration.) x In(1 + x) dx

Q: Evaluate the integral. (Use C for the constant of integration.) 64 + e* dx

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Q: Q2. Use Integration by parts to evaluate the following integrals Sear cosbx dx

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Q: Evaluate the given integral using the substitution (or method) indicated. (Use C for the constant of…

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Q: e*dx 5.

A: topic - integration by parts

Q: Evaluate the integral. (Use C for the constant of integration.) sin?(x) cos (x) dx

A: The given integral is ∫sin2πxcos5πxdx. Let u=πx. Then dx=1πdu. Solve the given integral using the…

Q: Find the indefinite integral. (Use c for the constant of integration.) [(4t³i (4t³i+ 14tj -7√tk) dt

A: The given integral is;  (4t3i +14tj -7(sqrt(t))k).

Q: Evaluate the integral: ∫6/[(x+a)(x+b)]dx for the cases where a=ba=b and where a≠b.a≠b. Note: For…

A: The integral, ∫6x+ax+bdx.

Q: a) Integrate the following expressions with respect to x. Then, find the value of the function…

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Q: Evaluate the integral. (Use C for the constant of integration.) S. x² – 16 dx x3

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Q: Evaluate the given integral. Use c as the constant of integration. e 22xdx

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Q: Evaluate the following integral: (Note that the constant of integration has been added for you.) | =…

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Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) dx…

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Q: Evaluate the integral. (Use C for the constant of integration.) 1000e p000.1x dx

A: please see the explanation below

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x'…

A: We calculate the given integral by substitution.

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: We have to solve

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 9 cos?x sin 2x dx

A: This question is based on Indefinite Integral.

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Use appropriate substitution and reduce the integration in easy form then solve it.

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Here we have to find the Given integral using substitution method.

Q: Integrate the following integrals using either integration by parts or integration by substitution.…

A: The given integral is ∫xsin1+x32dx. Take u=x.  Then, du=12xdx⇒du=12udx⇒dx=2udu Note that,…

Q: Evaluate the integral. (Use C for the constant of integration.) sin 70 de

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Q: A. Evaluate the following integrals using the different methods of integration dx 1. (9 + x²)3/2

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Q: Evaluate the given integral using the substitution (or method) indicated. (Use C for the constant of…

A: Using substitution u=4x-5

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: The given integral is,

Q: Evaluate the integral. (Use C for the constant of integration.) ∫(36dx/ (36 + e^x))

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Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: We have to solve

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: To calculate the integral

Q: First make a substitution and then use integration byparts to evaluate the integral.   ∫Cos √x dx

A: Given: I=∫cosxdx for evaluating given integral, we substitute x=t…

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: Given,

Q: Evaluate the integral ∫e^(2x) sin(e^x) dx, by first making a substitution and then using integration…

A:

Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) dx…

A: To find out the integral.

Q: (3x5 - 2x - 1) dz. dx

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Q: Q4. Using appropriate substitution, find the following integrals using the method of integration by…

A: We use the following results ∫u(x)v(x)dx=u(x)∫v(x)-∫(ddxu(x))(∫v(x)dx)dx ddxe1x=e1x×(-1)x2=-1x2e1x

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Consider the expression 3x2-2=u. The power rule of differentiation states that d dx(xp)=pxp-1, where…

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the…

A: We have to find

Q: Find each integral by integration by parts or a substitution, as appropriate. (Use C for the…

A: For part (a): Substitute u = x2 then the given function become:

Q: Evaluate the integral. (Use C for the constant of integration.) e^−θ cos(3θ) dθ

A: ∫e-θcos3θdθ We need to Evaluate the integral Using C for the constant of integration.

Q: Use integration by parts to find the integrals shares e) f sin? @ de f) esint sin2t dt 8) x²e-* dx…

A: Evaluation of the Integrals

Q: Q5. Use integration by part to evaluate ſešx sin (e4x )dx

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: u=7+x4  .........equation (i)differentiate wrt x on both side dudx=4x3du=4x3dxdu4=x3dx…

Q: Evaluate the integral. (Use C for the constant of integration.) 5 cos?x sin 2x dx

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Q: Evaluate the integral. (Use C for the constant of integration.) (5 + e) dx e

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Q: Evaluate the integral -6 dx (x+ a)(x + b) for the cases where a = b and where a + b. Note: For the…

A: Given equation is : ∫-6x+ax+bdx Solve the integration when a=b

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) + 9…

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) |…

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Q: Q2. Use Integration by parts to evaluate the following integrals Seax cosbx dx

A: Answer

Q: Evaluate the given integral as indicated: Use Integration by Trigonometric Substitution x³ dx 5 (4x²…

A: Given   ∫x3dx4x2+152 Use substitution as  4x2+112=sinθ to solve the given integral.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) |…

A: ∫x2 x3+7 dx -1u=x3+7du=3x2dxdx=du3x2

Q: Evaluate the integral. (Use C for the constant of integration) (X^7)/(e^3-5x^8) dx

A: