(e) ] 1 x2 _ 5+6 dx

Q: Factor x* + 1 as a difference of squares by first adding and subtracting the same quantity. Use this…

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Q: (21 + V3)/3 11 dx Evaluate 50 + x - 14x

A: Explanation of the answer is as follows

Q: How would I solve this problem using the product rule?

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Q: Find [(42³ + 3x²) da dx + C

A: The given integral is

Q: 5.[(2√x -3x)² dx

A: Given, ∫2x-3x2 dx

Q: x +4 x² + 2x + 5 -dx

A: To calculate the integral ∫x+4x2+2x+5dx.   Use the common integrals:…

Q: [ 3 -dx 33 + 1 ]

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Q: S(4x3 + 9x² + 4x – 1)dx -

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Q: (ど4ー) 2dx 4 X(3(Inx)*+121nx-15)2 2)

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Q: 3х -1 dx /3x²-2x

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Q: (√3-3)/6 - (√3+3) /6 12 dx 2 1+ (2x + 1)²

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Q: Calculate (3+1 x3+x a) using partial fractions b) using the substitution w = x3 +x

A: a) Given : ∫3x2+1x3+xdx  By Partial fraction  First, factor the denominator, we get 3x2+1xx2+1 =…

Q: dx 4 (7-x²)*

A: We will find the integral as following.

Q: tan-13x dx 1 + 9x2

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Q: Determine the following: iffere (a) 10 -5x² - 42x+194 (x+3)(x-8)(x-2) 9 -dx VIM

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Q: (x2 - 4x + 4)4/3 dx -

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Q: S sec²(3 – 2x)dx

A: ∫sec23-2x dx Put, 3-2x=t⇒0-21=dtdx⇒-2 dx=dt⇒dx=-dt2

Q: Evaluate: [8zº · sec² (25) dx =

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Q: | In (x²- 2x-8) dx 5. ら

A: Explanation of the answer is as follows

Q: e-) 1-2x - x2

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Q: 3 Evaluate: ((5x* – 2x' + 3x – 4)dx 3 S(-x'- + 4х -1)dx Evaluate: 1

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Q: dx V 20+8x x2

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Q: 20 x3 25+x² 2)골 2 dx

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

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Q: хt — х +6 dx х3 + Зх

A: We shall use polynomial long division method to simplify our integrand.

Q: 1 dx 5x² – 3 Find |

A: ∫1x5x2-3dx

Q: 3 What is the value of -8e -2x+1 dx?

A: Consider the given integral

Q: A = - 1)³² dx - (x - 1)³dx + 5²0x

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Q: 2. Use Theorem 4 to evaluate (3x +2x2) dx

A: Given ∫01 (3x+2x2)We know that ∫xn=xn+1n+1+C

Q: (5) Evaluate 75 2x -dx. 5x8

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Q: 3log; x (16x² – 6)1²dx =

A: It is known that ∫xndx=xn+1n+1+C, where C is the integration constant.

Q: -dx. Evaluate ſ &-3)(x*-1) ,. х2-2х-3

A:

Q: Find the intergral of (5-4x)/(√(12x-4x^2-8) ) dx

A: It is given that,               (5-4x)/12x-4x2-8dx     we have to integrate it.

Q: 15 S(+ 15e15x – 15x-1 + 15n) dx. x-14

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Q: (9+3)/3 13 dx ce 2 10+x-6x 3.

A: