By using u = In x, evaluate the integrals In x dx.

Q: x3 . In x dx

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Q: Use integration tables to find or evaluate the integral.

A: We have to evaluate the integral: ∫x4+5x2dx Assuming, t=4+5xx=t-45 Differentiating,…

Q: Express the integral in terms of the variable u, but do not evaluate it. In x -dx; u = Inx e3 rel4…

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Q: Evaluate the integral by integration by parts: TT √3 x² cos x dx

A: To evaluate the given integral by using integration by parts.∫0π2 x2 cos x dx

Q: Evaluate the integrals using integration by parts. ∫tan-1 y dy

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Q: Evaluate the integrals in ∫x2(x2) dx

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Q: Use integration by parts to evaluate the integral: In(s)ds

A: Given, To Evaluate

Q: Evaluate the integral using tabular integration by parts. (3 x² – x + 1) e¬¤ dæ +C -

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

Q: Evaluate the iterated integral. LLL* dz

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Q: evaluate the given integral.

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Q: Evaluate the integral. In(Vx) dx

A: Solution:

Q: Evaluate the integrals using integration by parts. ∫ (x + 1)2ex dx

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Q: Consider the integral (In(x))° dx:

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Q: Use the properties of integrals to verify that 2 < V1 + x² dx <2/2

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Q: Evaluate the integral: (In z) dz =

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Q: Evaluate the integral using integration by parts where possible. r In(8r)dx

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Q: Evaluate the integral S dx x In x

A: Given, ∫1x ln(x)dx

Q: 37. x² In x dx

A: To evaluate the integral ∫1e2 x2 ln x dx using integration by parts.

Q: Find the integral. Show work. Inx dx

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Q: Evaluate the given integral. Use integration by parts 4x' In(5x)dx

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Q: Evaluate the improper integral |. 3.x dx or show that it diverges. +1 x?

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Q: / In(1+ Væ)

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Q: Evaluate the integral. In x3 dx 15)

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Q: Evaluate the integral using integration by parts 2x e 5x

A: I=∫uv.dv=u∫vdv-∫du∫vdv where u is first function and v is second function

Q: 28. e cos 2x dx ,3x

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Q: S. v cos (x*) dx dy

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Q: 5 .Use the definition of the integral to evaluate | (2x - 3)dx

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Q: In x dx

A: The given integral is ∫-11lnxdx  If f(x) is continuous on [a, ∞) then the improper integral is…

Q: Evaluate the integrals using integration by parts. ∫eθ sin θ dθ

A: ∫eθsinθdθ

Q: Evaluate the integrals using the substitution method of e8x dx

A: To evaluate the integral: ∫e8xdx Solution: Let substitute t=8x. Differentiating both sides, we get…

Q: x$ - Inx dx

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Q: Evaluate the integral using integration by parts with the indicated choices of u and dv: 9х In(х)…

A: we use the formula integration of uv= u integration of v -integration of {du/dxintegration of v }.…

Q: Evaluate the integral using lIntegration by Partsisubstitution, or both if necessary. In(In 10x) dx…

A: Rewrite the given integral as shown below: ∫lnln10x10xdx=110·∫lnln10xxdx

Q: x Inx dx

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Q: Evaluate the integral. ∫ In (2x + 1) dx

A: It is given that,∫ln2x+1 dx We have to evaluate it.

Q: Evaluate the integral using integration by parts x2 In (x)dx 1

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Q: Evaluate the integrals using integration by parts. ∫t2 cos t dt

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Q: Evaluate the integral a* In(x) dr

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Q: Evaluate the integrals using integration by parts. ∫p4e-p dp

A: ∫p4e-p dp

Q: .2 32. 8x dx, x > 8 -

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Q: Find the integrals using integration by parts. b. [ Vx In /xdx

A: Consider the given: ∫xlnxdxIntegration by parts:∫udv=uv−∫vdu

Q: Evaluate the integrals by using a substitution priorto integration by parts. ∫x√(1 - x) dx

A: Here given as I=∫x1-xdx let  1-x = t Thus -dx=dt

Q: Evaluate the improper integral. x In6x dx 0.

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Q: Evaluate the integral using integration by parts with th xex dx; u = x, dv = e3x dx 3r 1 3x

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Q: Compute the integral by algebraic substitution:  ∫3x^5√16-x^2 dx

A: The given integral is: ∫3x516-x2 dxLet, I=∫3x516-x2 dx⇒I=3∫x516-x2 dx    -1

Q: dx (5 x)3

A: This question is related to definite integral, we will use the Integration by substitution method to…

Q: HEvaluate the integral 3 In

A: Given

Q: Evaluate the integral by reversing the order of integration. So Soy e dædy =

A: Given: ∫01∫8y8ex2dxdy

Q: Evaluate the integral using tabular integration by parts. |(4 2 – x + 2) e* de +C

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Q: Evaluate the integrals using integration by parts. ∫θ cos πθ dθ

A: Given: ∫θcosπθdθ