Evaluate the integral f 2x (x? + 1)“ dx using the substitution u = x2 + 1.

Q: Evaluate the integral. 4 dx Vx (1 +4x) X,

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Q: Calculate the integral in terms of the inverse hyperbolic functions.

A: To make the answer in inverse hyperbolic form, do the following substitutions. Substitute x=sint in…

Q: Find the indefinite integral.

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Q: Evaluate the integral or show that it is divergent.

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Q: Evaluate the integral. inegral (5x +1 )/(2x +1 ) (x-1 ) dx

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Q: Evaluate the integral. inegral  0 to 1    [ (x-4) / ( x2  - 5 x +6 )] dx

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Q: find the integral of dx 1- Sink

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Q: Evaluate the indefinite integral. V 16 +x² dx %3D to

A: We need to integrate ∫16+x2x4dx

Q: Evaluate the integral. x sec2(8x) dx = +C

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Q: Evaluate the integral

A: To integrate,

Q: Evaluate the integral. 2х + dx J1

A: We have to evaluate the given integral.

Q: Use u-substitution to evaluate the integral: x/(x+2)^3   dx

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Q: Evaluate the integral. dx 3 x+Vx² + 27

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Q: Evaluate the integral of x sin x² dx from x = 0 to x = VT.

A: Given,         The integral of xsinx2dx from x=0 to x=π .

Q: Evaluate the integral. inegral  0 to 1 [(x 3 -4x -10 )/(x 2 -x-6 ) ]dx

A: Consider the following definite integral:…

Q: Use substitution to find the indefinite integral

A: Given, ∫2+lnxx dx

Q: Evaluate the integral / f(x) dx, where -1 -{ if – 1 < x < 0 if 0 < x < 1 -X - f(x) = 1-VT - x²

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Q: -1 tan 2y dy

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Q: Evaluate the integral. dx 2x – 1

A: Let 2x - 1= u hence, 2dx = du Or, dx = du/2 when x = 2; u = 2 x 2 - 1 = 3 when x = 5 ; u = 2 x 5 - 1…

Q: Evaluate the integral or show that it is divergent.

A: Given: I=∫2∞dxxlnx                           ..1 for evaluating given integral, we substitute lnx=t…

Q: Evaluate the integral v22 -6x? dx V1- x2

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Q: Evaluate the integral f 2x (x² + 3)° dx using the substitution u = x2 + 3.

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Q: dx%3D 9+x²

A: Solution is given below:

Q: 2x dx Vx+3

A: Topic = Integration Use∫xn dx=xn+1n+1+C

Q: Evaluate the integral. 1 x + dx J4

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Q: evaluate the integral

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Q: Evaluate the integral. inegral x4 /(x-1) dx

A: Given: ∫x4x-1dx

Q: Evaluate the integral or show that it is divergent.

A: The given integral is ∫1∞dx2x+13. Evaluate as follows.

Q: Evaluate the integral J x3 dx V64-x²

A: let I=∫x364-x2dx

Q: Evaluate the integral

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Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1) -

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Q: dx 1 Vx + x3

A: Answer

Q: Evaluate the indefinite integral: dx + C. %3D 6x4

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Q: X- S2 *dx

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Q: evaluate using the integral 34. tanx sec x dx II Expand

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Q: 2. Use reduction formula to evaluate the integral: fsins x dx.

A: Reduction formula

Q: Evaluate the integral: f/2 sin(4t-u) du dt

A: To evaluate: ∫π2π∫0tsin(4t-u) du dt

Q: Evaluate the integral. (Use C for the constant of integration.) 2 tan3(x) sec(x) dx

A: Let sec(x)=t sec(x)tan(x)dx=dt tan2(x)=sec2(x)-1 Substituting we get 2 int (t2-1)dt =2 (t3-t)+C…

Q: Evaluate the integral dx/2sqr(x+3)+x

A: Given that

Q: x – x dx J 1+3x² – 2x3

A: Given, The integral ∫x2-x1+3x2-2x3dx  We have to evaluate the integral using substitution rule.

Q: evaluate the defmite Integral га (X -2)dx 4.

A: Given integral:

Q: Evaluate the integral: dx V4 – x2 Jo

A: Given query is to find the value of the integral.

Q: Find the integral of f(x³ + 1) Inx dx

A: Given :∫x3+1lnx dx

Q: Evaluate the integral using trig substitution: ∫x2√(3+2x-x2) dx

A: The integral function is ∫x23+2x-x2dx

Q: Consider the definite integral. (10x - )x – 1) ex²-x dx Let u = 5x2 – x. Use the substitution method…

A: As per our company guidelines we are supposed to do only first question. Kindly repost the other in…

Q: Evaluate the integral using trig substitution: ∫√(1+x2 )/x dx

A: The integral function is ∫1+x2xdx.

Q: Evaluate the integral: x2 dx V1 - x6

A: Given integral is: ∫x21-x6.dx

Q: Find the integral. J (x³ + 4x– 3) dx -

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Q: /1- xº V1-x°

A: