The integral f(x) dx after a change of varia a. J f(2.5x +7.5)dx O b. 2.5 L 12.5×+75)dx C. f(5x + 5)dx

Q: (x+ 1)dx 2. Jx2(x- 1)

A: Given: ∫(x+1)x2(x-1)dx Simplify by partial fraction decomposition.…

Q: ¹In(1+x) -dx 0 X

A: Expand log series

Q: f(3x + 2)² dx

A:

Q: 3. dx (x²+1)² -3 d x XVX +3, dx x2

A: Evaluate the given integrals

Q: -9 dx (3x + 1)² 1

A: Solution: ∫1∞-9(3x+1)2dxTake the constant out=-9×∫1∞1(3x+1)2dx

Q: 7. Use substitution to evaluate ſ 2x(4 – x²) dx.

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Q: How is a hyperbola different from a parabola?

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Q: 5. Change of variable 2 x dx 3x+1 a.

A: Given function, ∫12x3x+1dx

Q: 2 S(4x3 + )dx x+1

A:

Q: x +1 8. J x(x+ 4)3 dx

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Q: x² – 10x – 5 dx |x- 1)-(x² + 1)

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Q: 3. X+1 (tah dx X-1

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Q: (2x³-9x²+2) dx from x = 6 to x = 11

A: Given: ∫2x3-9x2+2dx   from x=6 to x=11

Q: d x – 2x d -{2x° + x=°] dx 5. dx 6. 7. d 5x-1 dx

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Q: Evaluate tan (7x+1) sec³(7x+1) dx .

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Q: Evaluate ¹/2 1 3 — 1 dx.

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Q: 5x*dx V1 – x³ .5

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Q: 9. x² dx (1 – x²)3/2

A: Let's find.

Q: YOUR TURN 6 Find xV3 + x dx form Sub In be 1. 2.

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Q: X 4. f* - 2x² - 6x +1 2 x² - 2x-8 dx

A: We have to find the integral.

Q: Evaluate J dx √x(1+√x)

A: ∫1udu = lnu +C

Q: Find the following

A:

Q: Evaluate. (4x + 5x²) dx -2x dx 8. 9. dx 10. -5 for x 2

A: To evaluate: ∫-12(4x+5x2)dx Solution: We know, ∫xn=xn+1n+1+C    ..(1) Here, ∫-12(4x+5x2)dx On…

Q: 1-√x)³ 3 √x dx

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Q: S Vx + 3(x + 1)dx

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Q: 10 dx (х3-10х+5)1/3 -2

A: Given integral is ∫−2010x3−10x+513dx We have to evaluate ∫−2010x3−10x+513dx by trapezoidal rule. The…

Q: dx 3 /x + Vx

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Q: x³ +4x² + x – 1 dx 2 X 16. .3 2 1 x' + x'

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Q: A. Evaluate Inx dx. 2x B. Evaluate [(7x-10)dy dx. 0 x?

A: Note: Since you have posted multiple questions. We will solve the first question for you. If you…