53. Use the substitution u = x + 1 to evaluate the integral I dr.

Q: Evaluate the integral. 3. (In(x))² x3 dx 1

A: I am attaching image so that you understand each and every step.

Q: Evaluate the integral 169 S. 13 dx 3 x( In x)³

A: Given integral ∫13169dxx(lnx)3. The objective is to evaluate the integral.

Q: Estimate ë to five digits of accuracy by computing the integral of f(x) = 4/1 – x² for x € [0, 1].

A: Given fx=41-x2 and x∈0,1 I=4∫x=011-x2dx

Q: 9. Find the integral, using u substituti x-(1-3x²)*dx a.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Evaluate the integrals

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Q: Evaluate the integrals in ∫e√r/√r dr

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Q: Evaluate the integrals in ∫2ln x/x dx

A: Now put,

Q: 4 Write an integral that is equivalent to 1 af dx. -

A: Given,          ∫-6-4xf14x2-2dx

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫√(2x + 1…

A:

Q: Evaluate the integral from -n/2 to +t/2 of x² sin x.

A: Given integral

Q: Evaluate the improper integral, 5 if exists : dx (5 – x)3

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Q: Evaluate the integral (1² – 4z) dz using its definition.

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Q: 5. Evaluate the integral by using trigonometric substitution. x2 dx J Tx2 - 25 Vx² –

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Q: Use substitution to find the value of each indefinite integral. swers. x In et + 12 xp

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Q: 6. Evaluate the fallowing real integrals by residue theerem 3 2计 I = Ssine -d8;a>l anse 2(a- Ja?1)

A: Given: I=∫02πsin2θa+cosθdθ, a>1

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A: We need to integrate∫ex-8x-8dx

Q: dt (2 – t4)4 -1

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Q: Which integral could be evaluated using the substitution u = x ?

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Q: Evaluate the integral (ez – 107) dr

A: Solve the following integral

Q: Use thě substitution a = 7 tan(0) to evaluate the indefinite integral 40dx x²Væ² + 49 +C

A: Substitute x=7tanθ After differentiating, dx=7sec2θdθ

Q: u= 4-xneduce the ntegral to standand ferm Sonm dx 4-x)=

A: ∫x64-x72dx In this problem we need to reduce the given equation into standard form and solve the…

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

A:

Q: 5) Evaluate the integrals using appropriate substitutions a) sec 2x tan 2x dx b) 2x+1

A: Given that, a) ∫sec32x tan 2x dx b) ∫x2x+1dx For evaluating those indefinite integrals,  we need to…

Q: Compute this improper integral showing all steps.  integral of (x/(x^4)+9) dx from 0 to infinity.

A: please refer to the image below

Q: Evaluate the integral: |(322 + 1)(x³ + x+2)*dx

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Q: Evaluate the Integral / tanh (2x)đx. A @ --n|cosh(2x)| + C B -In|cosh(2x)| + C © 21n|cosh(2x)|+ C D…

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Q: fxVx+5 dx :

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Q: Find the indefinite integral.

A: The given indefinite integral is ∫6z9z2-25dz.

Q: Evaluate the improper integral attached with this question.

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Q: Evaluate the indefinite integral by using the given substitution to reduce the integral to standard…

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Q: Evaluate the integral: S (in ce) dx = (8 ln(x))²dx 2 (x8) ( ×

A: Evaluate ∫lnx82dx=?

Q: Evaluate the given integral with suitable substitution : (36z + 36) dr

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Q: +00 dx Evaluate the improper integral x(In x)²

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Q: de 1+tan 0 k/2

A: Let I=∫0π2dθ1+tan θ      I=∫0π2dθ1+sin θcos θI=∫0π2cos θ dθcos θ+sin θ     ....(1)Using property…

Q: Use reduction formulas to evaluate the integrals ∫ 8 cot4 t dt

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Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ dt/t4 + 4t2 + 3

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Q: Evaluate the integral(mx+b)/(x-p)(x-q) In the integral m,b,p,q are constants and p is not equal to…

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Q: de 2/2 V5 9 18

A: Solution: Here let I=∫dxx29-x2 Substitute: x=3sinu u=sin-1x3 and dx=3cosudu Thus,…

Q: 1. Evaluate (2 – x) dx by drawing a picture and interpreting the integral in terms of areas.

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Q: Evaluate the integrals in ∫ex/2 dx

A: To evaluate ∫ex2dx

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

A:

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: Evaluate the integrals by subs;tu;on dp- V5+x c)

A: ∫-14x5+x dx

Q: dx Vre(16/:

A:

Q: Use the Midpoint Rule to evaluate the integral S x² In(x² + 1)dx O 2 In(4) O 4 In(5) O In(10) O 2…

A: Given integral is ∫02x2lnx2+1dx. We have to evaluate the given integral by using midpoint rule.…

Q: evaluate the improper integral from 1 to infinity: 2/[x(x+2)] dx

A:

Q: Q5- Evaluate the integral, x(In x) Jo(x)dx

A: The expansion of the function J0x is  J0x=∑n=0∞-1nx2n22nn!2                 (i) Multiplying x ln x…

Q: /1- xº V1-x°

A:

Q: Suppose we perform the substitution .3 u=9-x in the integral

A: Given that:∫123x29-x3dx