Evaluate the integral √(4 by making the appropriate substitution: u √ (432² dx [ X (4x² + 11) 7 = X (4x² + 11) 7° dx +C

Q: x³ dx 9+x* 1.

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Q: S. FInd (4x3 + 3x2 – 2x + 1)dx ·

A: The given integral is as follows:  ∫014x3+3x2-2x+1dx We shall evaluate the value of the integral…

Q: Evaluate (2x² - 4x + 1)² dx. √

A: Given data:- ∫x32x3-4x+12dx

Q: S Vx8 – 6x6 + 9x4 dx is equal to -

A: The equation of integral is ∫x8-6x6+9x4dx.

Q: x2+1 - dx x4-x²+1

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Q: .2 dx Jo (9 + x²)2

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Q: Show that (xcos(2x)dx=. A-2 8

A: LetI=∫0π4xcos2xdxPut 2x=udifferentiate on both side2dx=dudx=du2As x→0 then u→0As x→π4 then…

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

A: See the attachment

Q: Evaluate /x* V5 - x*dx

A: We have to evaluate the integral: ∫x35-x2 dx Rewriting the integral, ∫x35-x2 dx=∫x2x5-x2 dx Now…

Q: Compute the following. S(24x-8) (24x -8)(6x²–4x – 9)ª dx

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Q: Compute 3+r+1 dx x2

A: Given : ∫233x2+2x+1x2dx

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

A: we use integration by parts

Q: Evaluate.

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Q: A = - 1)³² dx - (x - 1)³dx + 5²0x

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Q: Find ∫ √(3 − 5x) /2x   dx.

A: Consider the given integral, ∫3-5x2xdx substitute 3-5x=u ⇒ dx=-23-5x5 ∫3-5x2xdx=2∫u2u2-3du now,…

Q: Evaluate x(x2 + 1)3 dx.

A: Given ∫x(x2+1)3dx

Q: Compute the following. d [(3x11+5x7-12xª+16x²+28x)(7sec(x)-5x-4–14)] dx

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Q: 1. Evaluate : S (4x* + dx 2 S"(4x³ +)dx 0. x+1

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Q: te the following: 2x dx x - 4 dx

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Q: Q.2: Evaluate: -2 2 dx 1 I = x2 - 8.

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Q: 2x² − x +4 x³ + 4x Evaluate [ [20 dx.

A: Evaluate