-Find the value of th integral e-x' dx.

Q: Evaluate the integrals ∫(ln x)-3/x dx

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Q: Find the integral of (e^x - 1)/(e^x + 1) dx.

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Q: 4. Evaluate the improper integral dx +e"

A: We know that, ddxex=ex ∫1a2+x2dx=1atan-1xa+c tan-1(1)=π4 tan-1(∞)=π2

Q: Find the indefinite integral.

A: To evaluate the integral: ∫ex+e-xex-e-xdx Solution: Given,…

Q: 2. Compute the indefinite integral xe dx

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Q: 2x e dx +1 2x

A:

Q: Find the integral of x^2 * cos(4x) dx.

A: To compute the indefinite integral.

Q: Find the indefinite integral ∫ e5x−3 dx

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Q: Find the indefinite integral.

A: Let ex+e-x=v. Differentiate both sides: (ex-e-x)dx=dv Substitute v and dv in the integral…

Q: 1 Find the indefinite integral || e* + dx 1+x?

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Q: Find the indefinite integral ∫ e−x4(−4x3) dx

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Q: evaluate the given integral.

A: Use Substitution method to determine the value of  integral .

Q: Find the indefinite integral ∫ e1−3x dx

A:

Q: 3. Find the indefinite integral: Sx(x-2)* dx

A: Please rate

Q: Evaluate the integral. | (e7* +3e -x) dx 7X +3 e -X) dx=

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Q: S dx 2.

A:

Q: What is the integral of ((x^2)*e^(3x))dx from 0 to 1?

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Q: 7. Evaluate the improper integral. -kx e (k: constant)

A: Please refer to the image below.

Q: Evaluate the integral.

A: Given: ∫ex1-e2xdx

Q: Integral from 1 to e of 5t^2 lnt dt

A:

Q: Compute the integral 1 dx. x + x ln²(x)

A: dln(x)dx= 1x∫11+x2=tan-1x+c

Q: Find the indefinite integral ∫ e2x/(1 + e2x) dx

A: Given: I=∫e2x1+e2xdx for evaluating given integral, we substitute 1+e2x=t…

Q: Find the indefinite integral. e2x dx 4+e4x

A:

Q: Find the indefinite integral

A: Explanation: Given that,  ∫e2x4+e4xdx   Substitute  e2x=ue2x(2)dx=due2xdx=du2 Now 12∫14+u2duNow put…

Q: Evaluate the improper integral e-1/x dx

A:

Q: Find the indefinite integral.

A: Consider the given: ∫ e-x4-4x3dx=∫ -4e-x4x3dx=-4·∫ e-x4x3dx

Q: Find the integral of- :(e*-1) dx. (ex+1)

A: Simplification of the given function helps to find the required integral. Substitution of the…

Q: Find the indefinite integral. x' + dx +C.

A: Integrate

Q: Find indefinite integral.

A: Given integral: ∫x3e3x4dx Substitute t=3x4 and differentiate it w.r.t. 'x'…

Q: Find the indefinite integral. 1 dx = +C. x +

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Q: Find the indefinite integral ∫ (e2x − e−2x) / (e2x + e−2x)   dx

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Q: Find the indefinite integral. 1 - e2x dx

A:

Q: Find the indefinite integral ∫ dx / x(ln x2)3

A: Given,          ∫dxxlnx23

Q: 1. Evaluate the improper integral 150 xe dx or state that it diverges.

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Q: Evaluate the integral S-21 (x+2)(x-1)dx

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Q: evaluate the given integral.

A: Solution:-The given integral is  ∫x+2(x-1)(x+3)dx since  x+2(x-1)(x+3) is solved by partial…

Q: Find the indefinite integral. x + 7x2 + e) dx

A: The sum rule of integration states that ∫a+bdx=∫a dx+∫b dx. The constant rule of integration states…

Q: e2x +2e* -dx e* +1 2.

A:

Q: Calculate the integral approximation S6 for 0 -1 4-² dx.

A: In this question we have to find the Integration.

Q: 6. Evaluate the integral e* dx ex + e-x

A:

Q: Find the indefinite integral ∫ (e4x − e2x + 1) / ex   dx

A: Here given as It can be written as

Q: Evaluate the integral ∫dx/x ln x

A: Since, our aim is to evaluate the integral given below:-∫dx(x ln(x)) -(i)

Q: How many times do you need to integrate by parts to reduce ff(In x)° dx to an integral of In x? ·

A: Given integral is ∫1eln x6dx

Q: Consider the integral (ln(x))6 dx:

A:

Q: Find the indefinite integral x2e +e² dx.

A: The given indefinite integral is: I=∫x2e+ex dx

Q: find Hhe integral of Jx ln (x*- 4) dx 2

A:

Q: Find the indefinite integral -dx (2-x ²)? dx = 2-x)?

A: To find the indefinite integral:∫x2-x22dx

Q: Evaluate the integrals in ∫ln 2 log2 x/x dx

A: ∫ln (2) *log2xxdxChange of base rulelogab=logcblogca Formula∫xndx=xn+1n+1+C

Q: Find the general indefinite integral.   ∫ (√ x3+  3√ x2)    dx

A: