Evaluate the integral in terms of (a) inverse hyperbolic functions and (b) natural logarithms. 5dx i x/9+ ( In x)²

Q: (x²-5) -dx J x3+15+12 c3.

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Q: Evaluate the definite integral two ways: first by a u-substitution in the definite integral and then…

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Q: Evaluate the integrals in Exercise  in terms ofa. inverse hyperbolic functions.b. natural…

A: To evaluate,

Q: Consider the indefinite integral a Vx² +1 da: This can be transformed into a basic integral by…

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Q: Evaluate the integral. (Use C for the constant of integration.) x2 - 81 xp

A: Let,I=∫x2-81x3dxI=∫x2-81.1x3dxI=x2-81∫1x3dx-∫∫1x3dxddxx2-81dxI=x2-81∫x-3dx-∫∫x-3dxddxx2-81dxI=x2-81x…

Q: Find the indefinite integral and check the result by differentiation. 4u? + 14и — 9 du u* 4

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Q: What is the integral of a function e raised to the power -n .?

A: topic- integration

Q: Determine whether the integral is convergent or divergent. *0⁰e-1/x +² [²² O convergent O divergent…

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Q: Evaluate the indefinite integral: du + C.

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Q: Can you use the Log Rule to find the integral below? Explain. ∫ x / (x2 − 4)3 dx

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Q: Determine whether the integral is convergent or divergent. If it is convergent, then evaluate its…

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

A: Here we have to evaluate,

Q: evaluate the indefinite integral.

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Q: Evaluate the integrals in ∫dx/x (log8 x)2

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Q: Evaluate the integral, if it exists.    ∫01 (1 -x9) dx

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Q: Sea(4 + e3*)-1 dx

A: Solving the problem by finding the solution of the integral.

Q: Evaluate the integral dx 4x log 2×

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Q: Evaluate the indefinite integral: ∫(θ + sec2 θ) dθ

A: Our Aim is to evaluate the indefinite integral given below:-∫θ+sec2 θ dθ  -(i)

Q: 34 1 dx (x – 2)3

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Q: Evaluate the integrals in ∫log10 x/x dx

A: Given integral is: ∫log(10x)xdx To evaluate this integral, first apply the logarithmic property…

Q: Evaluate the indefinite integrals - e2* )dx

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Q: Can you use the log Rule to find the integral below? Explain. (x²-4)3 dx

A: Explained below

Q: Use the Log Rule to find the indefinite integral. (Use C for the constant of integration.) dx

A: Let z=x2+2dz=2xdxxdx=dz2

Q: Evaluate the integral. dx + 4x + 20 5 log (2) – 2 log(5) – 4 + tan"

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Q: Use the Exponential Rule to find the indefinite integral. (Use C for the constant of integration.)

A: Integration is the process of finding the anti-derivative function of a given function. Integrating…

Q: Evaluate the indefinite integral. -dx 1 – x8

A: We use the standard integration result ∫11-x2dx=sin-1x+C

Q: 3x dx

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Q: find the indefinite integral of e^(x)sqrt(8-e^x) dx

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Q: Evaluate the definite integral. 8 dx 1

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Q: Determine whether the integral is convergent or divergent. 0. el/x 5 dx .3 -1

A: The given integral is is convergent , since the function inside the integral is continuous on the…

Q: Evaluate the integral. (ln(x8))2 dx

A: Apply integration by parts u = (ln(x8))2 and  v = 1:

Q: (log3×)" dx 1. log3 x)2

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the indefinite integral. (Use C for the constant of integration.) el/x6 xp-

A: integral, ∫e1x6x7dx

Q: 1 dx. x(1+ ln x)

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Evaluate the indefinite integral -dx x4 + 3

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Q: Find the indefinite integral. (Use C for the constant of integra -8 + 12 dx ャ

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Q: 33 = 1-

A: Here we evaluate the integral by using substitution method    ∫ dt/(1-3t)7 , u = 1 -3t

Q: Evaluate the indefinite integral:  x3ln(x2-1)dx

A: Given integral By using the following substitution, we get

Q: e doe

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Q: Evaluate the integral. 8 · log 16 (x+ 8) -dx x+8

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Q: Use a Table of Integrals to evaluate the integral. 2xdx Va4 +1 log la" + Vz +1|) Check your…

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Q: dx 322-2х + 5

A: Consider the indefinite integral ∫dx3x2-2x+5 To evaluate the indefinite integral, first complete the…

Q: The undefined integral of the function [1+ cos x} power -1 is *

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Q: sec dx Eanx

A: Given

Q: Evaluate the indefinite integral. x² A -dx 1- x6

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Q: Evaluate the integral: a log(1+x²)e- dæ

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Q: Evaluate the integral. (Use C for the constant of integration.) 9 - x xp

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Q: (2х-2 dx

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Q: x²-x x+1

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Q: Evaluate the indefinite integral. sec“(2x)dx

A: We use substitution method to solve this integration