7 In x (1) Evaluate the definite integral dx.

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

A: Consider I = ∫0∞e-x2 dx                              (1) Let x2 = t On differentiating both sides,…

Q: -cos² dx X' X

A:

Q: 4 18. Evaluate the indefinite integral / dx. 3 X,

A: Given integral to find ∫4x3dx To integrate this first take the constant out 4∫1x3dx Applying the…

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

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Q: 1 Evaluate the improper integral dx. (x – 3)3/2' 3 -

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Q: 6. Find the indefinite integral x² dx

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

A: Please rate

Q: 3. Evaluate the indefinite integral 1 -dx x' + 3x? 3

A: Given,

Q: Evaluate the improper integral 1 dx x - 1

A:

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

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

Q: 5. Find the integral 1 -dx x -5x +6

A:

Q: Find the indefinite integral. ∫(x2 cos x)dx

A: The given integral is ∫x2cosx  dx. Let u=x2  and   dv=cosx dx. This implies that du=2xdx  and…

Q: 4. Evaluate the indefinite integral. 24x³e(2x*) dx

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Q: =dx V2x* +3 4

A:

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

A:

Q: Evaluate the definite integral.

A: ∫15x2x-1 dx Consider, ∫x2x-1 dx Put, 2x-1=t⇒21-0=dtdx⇒2 dx=dt⇒dx=dt2 Therefore, ∫x2x-1 dx=∫t+12tdt2…

Q: Find the indefinite integral.

A: To find: The indefinite integral ∫dxxln x23. Concept used: Power rule of logarithmic: ln ab=b·ln a…

Q: Find values of p for which integral diverges. dx x(In x)"

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Q: 2) S (x³ - 7) dx

A:

Q: 2. Find the indefinite integral (Scos(4x) + √x dx

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Q: Evaluate : Integral from 0 to 2 : 2x^2 e^-2x dx

A: To determin the value of the definite integral.

Q: Find the definite integral from 1 to 3 of |-3x+1| dx

A: According to the given information it is required to find the value of the definite integral.

Q: dx 1. -1 V1 – 2x – x²

A: Explained below

Q: 8) Evaluate the Integral x2 + 2x dx

A:

Q: Evaluate the definite integral. 6. e2x dx e2x + 3

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Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

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

A:

Q: 15 Find the integral | 2/x (1+x) dx.

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Q: 4. Evaluate the integral: In6 -2x + sinh 2x|dx e2x + e-2x

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

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Q: 6. Evaluate the integral. x³e2x dx

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

A: Here given as It can be written as

Q: (a) Evaluate the integral [x (x* -1) ´dx by using substitution.

A: To evaluate the given integral ∫x3x4-12 dx by using substitution.

Q: Find the indefinite integral.∫cos2 3x dx

A: To evaluate the indefinite integral ∫cos23x. Solution: The given integral is ,∫cos23x Multiply both…

Q: 2 Evaluate the improper integral 4x e dx, if exists. 8.

A: Given that,           ⇒           ∫-∞2e4x dx   ,   if exist             ⇒         find the…

Q: Compute the definite integral 2 dx Vx² + 4

A: First, we need to compute ∫xx2+4dx

Q: Evaluate the integral ( sin(In(2+2x)) x+1 dx

A: Given: ∫sinln2+2xx+1dx

Q: Evaluate the definite integral: 1/5 dx 1-x2

A:

Q: Evaluate the integral.

A: Our Aim is to evaluate the integral given below:-I=1[cos(x)-1]dx     -(i)

Q: 2 1. Evaluate the integral: dx 2 x2-x

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Q: Evaluate the definite integral. 1 dx V2-x

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Q: 10. Find the indefinite integral. x – 2 dx x² + 1 -

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Q: In x dx

A: Given: ∫lnxx2dx Integrate the given integral using the integration by parts formula.

Q: 3 Evaluate the definite integral dx. (x- 5)4 -2

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Q: Evaluate the indefinite integral dx x(x²+2x+1)

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Q: 13. Evaluate the integral dx x – 1

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Q: 15. Evaluate the integral 10 ·dx (x – 1)(x² + 9)

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

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Q: Use U-Substitution to evaluate the definite integrals. Sž cos 2x dx (1+x2)2

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Q: 7 Evaluate the improper integral, if exists : dx (5 – x)3

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