Exercises 7 Evaluate: 2 (2x - 3)* dx 5 (2) J 1 dx 0*+3 (3) dx x + 9 x In x dx

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

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

Q: х2 — бх + 9 dx Убх — х2

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Q: 3 Evaluate 7x? dx 1 7 (Hint: f(x) = 72? and F(x) = a*) 3

A: The given integral is: ∫137x2dx Since, 7 is a constant, so take it out side. ∫137x2dx=7∫13x2dx The…

Q: Which is NOT included in evaluating the integral? (Use partial fraction decomposition method.) 4 2x…

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Q: Зx t2-1 dt dx '2x t2+1 d

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Q: Evaluate: (5x* – 2x + 3x – 4)dx |-

A: Consider the integral, ∫5x4-2x3+3x-4dx

Q: 5 S(4x² – 12x +9) ²dx

A: We use here binomial expansion and then we  integration.

Q: S dx 2 (1+x²)²

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Q: 3х -1 dx /3x²-2x

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Q: x2+1 - dx x4-x²+1

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Q: dx V4 - x - dx 2 8)

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Q: Q3. Integrate: ] x+4X*+4X

A: we have to solve :∫x+1x3+4x2+4xdx

Q: x-1 2 x² + x -dx

A: As per the question we are given an indefinite integral of (x-1)/(x2 + x) which we have to evaluate.

Q: 2. Integrate the following: /(x (x² + 7)*)dx a. 8x(x³ + 7)³(3x²) + c x³ ((x³ + 7)° + c 5 b. 3 (x³ +…

A: It is given that, ∫x2(x3+7)4dx   Here this integral can be solve by using substitution method.…

Q: a

A: Here we have to evaluate I=∫xex1+exdx ...........................(1)

Q: Lt² V4-t² dt V(4-x)/(2\x) x(4-x)

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Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: x´ + 2x x' - x + x - 1 -d- .3 2

A: Given integral is ∫x2+2xx3-x2+x-1dx

Q: (2x–1)4 y = (a²+1)³ ,3 y = xe*°

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Q: Evaluate: 2 (1) (2-3)* dx 1 1 dx x + 5 (2)

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Q: S 1 dx (2x - 3)²

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Q: +9 J4 (12x² - 8x+10) dx

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Q: dx Evaluate

A: ∫0919+x2dx

Q: (3x³ – 2x² + x -5) 1. dx (Hint: Simplify the integrand first) 4x2

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