dx (6-x²)3/2 S"_ tan (x)dx

Q: Find the following indefinite integral: ∫12x (x2 – 9 )-3 dx. Hint: Use a Substitution

A: Given: I=∫12xx2-9-3dx for evaluating given integral, we substitute x2-9=t…

Q: e2x sin 2x dx

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Q: Evaluate the following integrals using Trigonometric Substitution: x-1- 16x dx x 2. dx 9 dx 25t2 - 1…

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Q: Evaluate the following integrals x3+1 dx x3-x

A: We have to evaluate the integral ∫x3+1x3-xdx.

Q: Approximate the following integrals using the Trapezoidal rule. r0.35 2 dx x2-4 1. 2. Sfx sin(x) dx…

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Q: Evaluate the following definite integral using substitution rule Só 2x /x² + 2 dx 1.

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: [ (2x+6)*dx 3.

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Q: Evaluate the following integrals.

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Q: 4. dx (x² +1)*

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Q: Evaluate the following Integrals 1 I. dx 1-cos x

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: S sin x e cosxdx

A: The objective of the question is evaluate the given indefinite integral using substitution method.

Q: e*dx е 2x+1 e

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Q: In x dx Sx² sin x dx S(x + 2)vx +1 dx

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Q: Sx² tan x3 dx (In x)3 dx 4x 2x3 dx x++1

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Q: 4x Use the appropriate substitution to evaluate the following integrals: dz =.

A: To find:∫4xx2-1dx

Q: Evaluate the following definite Integrals by using Gamma or Beta Functions: x² So (1+x6) ³ dx

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Q: 4x dx 1+ x²

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Q: Evaluate the following integrals S²z sin³ x cos20 x dx 2

A: We have to evaluate the integral ∫-π2π2sin3x cos20x dx.

Q: Evaluate the following integral by using the appropriate substitution cos (x) dx 4 sin(x) + 2

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Q: dx (6-x²)3/2 TT

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Q: 2. dx

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Q: Evaluate the following integrals: dx dx dx ii) S 2 sinx+8 cos x a sinx+b cosx 1+tan x

A: (i)

Q: Which of the following integrals are improper? (Select all that apply.) 1 dx 6x dx 2x - 1 sin(x) dx…

A: We have to find out the improper integral from the given options

Q: Vex – 1 dx c2

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Q: -4x dx | xe

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Q: 9-x2 dx. Use trigonometric substitution. x2

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Q: Determine the following integral by making an appropriatesubstitution.

A: Given∫cos3x2-sin3xdx

Q: 2. x² V1-x? dx_

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Q: Use the table of integrals at the back of the text to evaluate the integrals ∫dx/x√x - 3

A: To evaluate the integral: ∫1xx-3dx. Let substitute u=x-3 dudx=12x-3dx=2x-3du Substituting the value,…

Q: dx 3 x (1+ Vx)²

A: according to our guideline we are supposed to answer only the first question if you want any…

Q: Evaluate the following integrals. 1) La7 dx Ans. 4 1 v1-2x-x2

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Q: tan 2x dx 2. S (3+ln cos 2x)6

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Q: 9— е2х dx a.

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Q: 1 36* dx V6* + 3 2x dx x2 + 2x + 5

A: The given integrals are: ∫0136x6x+3dx and ∫2xx2+2x+5dx

Q: 4 x*dx X-1

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 6. Evaluate the following integrals: (a) /sir sin³ x dx

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Q: Evaluate the following integrals. Show all the necessary solutions. ² dx 1.

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Q: Evaluate the following definite integrals using substitution: jx(1-6x* )'dx

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Q: (x+1)dx x²-3x+5

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Q: 1 dx 2 х3 — х3

A: Given: I=∫1x23-x13dx   ...1   We know that; ∫1ax+bdx=1alnax+b+C

Q: Evaluate the following integrals using the tabular method. (i) 2x sin 2x dx

A: We need to evaluate the integral ∫e2xsin(2x)dx by tabular method

Q: 4. tan³x sec*x dx. Use trigonometric groups

A: To evaluate the value of: I=∫0π4tan5x sec4x dx=∫0π4tan5x sec2x sec2x dx=∫0π4tan5x(1+ tan2x) sec2x dx

Q: sech x3 tanh x3 iii. S- dx

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Q: Evaluate the following Integrals dx cosx 5+ +anx X.

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Q: vi. Sz sin³ x cos20 x dx 2

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Q: Evaluate the following Integrals: 1. 6x² sin x³ dx

A: NOTE: As per our guidelines, I have solved the first problem in the picture.

Q: Evaluate the following integral by using Odd and Even Powers Method: y = [ cos³ (;x) dx

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Q: Evaluate the following integrals using Trigonometric Substitution: 1. X-1- 16x dx

A: Given integral: ∫x1-16x2dx