Evaluate the integral J*(x*-1)°dx by using substitution.

Q: Vx² – 1 -dx

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Q: cosh cosh 1x dx

A: To Determine: find the integral  Given: we have ∫cosh-1xdx Explanation: we have integral ∫cosh-1xdx…

Q: 5+x*dx

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Q: Evaluate the integral or show that it is divergent.

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Q: Evaluate the integral using Algebraic Sub. Vax dx Vx -

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Q: Evaluate the integral. inegral (5x +1 )/(2x +1 ) (x-1 ) dx

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Q: Evaluate the integrals ∫2tan x sec2 x dx

A: Now put

Q: Use the limit form of the definition of the integral to evaluate the integral, (3 – 2x) dx. Show all…

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Q: xarctanx dx

A: Product Rule of integration : ∫u.v dx = u∫vdx - ∫(dudx∫v dx)dx darc tanxdx = 11+x2 ∫ xn dx =…

Q: Evaluate the integral or show that it is divergent.

A: Given: An integral

Q: ( 3.x³ – 2x³ + 5x² – 2 x3 + 1 dx

A: Given integral is improper fraction form so we need to apply long division method to convert it into…

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

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Q: Evaluate the integral by using a substitution prior to integration /2s + 17

A: Here we have to evaluate,

Q: 37. x² In x dx

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

Q: Evaluate the integral using trig substitution: ∫√(x2+2x) dx

A: The integration to be performed is I=∫x2+2xdx. Substitution method will be used to solve the…

Q: Use a substitution method to evaluate the integral

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Q: Use the Table of Integrals to evaluate the integral.

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Q: Evaluate the integral. inegral  0 to 1 [(x 3 -4x -10 )/(x 2 -x-6 ) ]dx

A: Consider the following definite integral:…

Q: Evaluate the improper integral if it exists 1 dxp:

A: We have to use properties of integration.

Q: evaluate the integral from 0 to sqrt(2) x2/(4-x2)3/2 dx

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Q: x sec (3x) tan (3x)dx

A: The given integral is ∫xsec3xtan3xdx. We know the integration by parts formula:…

Q: Evaluate the integral or show that it is divergent.

A: Given: I=∫2∞dxxlnx                           ..1 for evaluating given integral, we substitute lnx=t…

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

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Q: dx X-1

A: Given : ∫xx-1dx

Q: xsec.

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Q: 2x dx Vx+3

A: Topic = Integration Use∫xn dx=xn+1n+1+C

Q: The improper integral 5dx is V1-x?

A: Since you have asked multiple, we will answer the first one. ∫015dx1-x2dxLet x = sin θ ⇒ dx = cos θ…

Q: 00 1 -dx x3 – 1 1 4

A: Use the definitions of improper integrals to write the improper integral in terms of limits.

Q: Evaluate the integral, if it exists: +z sinx dx z-

A: We will evaluate the integral if it exists in the following step.

Q: Evaluate the integral or show that it is divergent.

A: The given integral is ∫1∞dx2x+13. Evaluate as follows.

Q: Evaluate the integral using appropriate substitution: (ii) x^2√(1 + x)dx

A: Let the given integral be y - y = ∫x21+x dx         ..................(1)Let,u2 = 1+x…

Q: Evaluate the integral using integration by parts. 2x dx (5x2 - 12х) е 2х

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

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Q: tan (5x) sec2(5x) dx

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Q: 1 dx 1+ Vx 3

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Q: evaluate using the integral 34. tanx sec x dx II Expand

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Q: x – x dx J 1+3x² – 2x3

A: Given, The integral ∫x2-x1+3x2-2x3dx  We have to evaluate the integral using substitution rule.

Q: Evaluate the integral. inegral  ax / (x2 - bx ) dx

A: Consider the given integration as I=∫axx2-bxdx⇒I=∫ax-bdx

Q: Use the Table of Integrals to evaluate the integral.  ∫01x4e-x dx

A: Given:∫01 x4 e-x dx∫u dv=uv-u'v1+u"v2-u'''v3+u''''v4-.......

Q: Evaluate the integrals ∫cot3 x dx

A: We have to evaluate the integral: ∫cot3 x dx Rewriting the integral, ∫cot2 x cot x dx We know the…

Q: Evaluate the integral.

A:

Q: Evaluate the integral.

A: Given: The integral, ∫12x5lnx dx.

Q: dx Va(x+1)

A: the given integral is: ∫14dxxx+1 we have to evaluate the given integral.

Q: Evaluate the integral. In 2 tanh x dx

A: ∫02tanhx dx=∫02sinhxcoshxdxUsing formula ∫f'(x)f(x)dx = ln|f(x)| +cHere , f(x)=sinhx , f'(x)= coshx

Q: HEvaluate the integral 3 In

A: Given

Q: 1/3 0 4x dx √25-x

A: Given Problem:- ∫0134x25-x4dx

Q: Evaluate the integral using appropriate substitution ∫(x^2 +1)/(√(x^3 +3x))dx

A: Given an integral: ∫x2+1x3+3xdx Let, x3+3x=t t=x3+3xdt=3x2+3dxdt=3x2+1dxdt3=x2+1dx Substitute value…

Q: Evaluate the integral.  integral   csc x  dx

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Q: Evaluate the integral ∫ x3ex dx

A: Topic-integration

Q: the

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