The following integral can be evaluated by using substitution: a) b) c) Identify the inside function. = Differentiate: Factorise this: Rewrite the whole integral in terms of u and du: f Simplify and cancel a² +5: f Integrate with respect to u: Hence write down the indefinite integral: du 4 (2²+5) (2³+ 15z)³ dr du [4 (2²+5) (2³ +152)³ dz (Don't forget the constant of integration as this is an indefinite integral.)

Q: Evaluate the integral by making the appropriate substitution: u = 38 fa² (2³ − 1) ³ dx = [ - 38 fx²…

A: Topic = Integration

Q: Use the technique of completing the square to evaluate the following integrals. 163. 1. .2 + 10x

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Q: Evaluate the integral: ³√25x²dx √2³ √25 - 22²

A: The given integral

Q: Evaluate the integral: (9si + 15sj + 4k) ds k i+ j+ Answer:

A:

Q: Evaluate the integrals of the following: (Show clear and clean solutions) T sec2ysin4ydy

A: We need to solve the integration.

Q: a – 5x3 + 6x2 - 18 (ii) dr a3 – 3x²

A: Using integration

Q: dr V9+ 8a-a2

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 24. Solve the following integral using substitution method: f8x√2x² - 1dx

A: Sol:- ∫ 8x2x2-1dxTake the constant out:  ∫a·fxdx=a·∫fxdx=8·∫ x2x2-1dxIntegral Substitution…

Q: Evaluate the integral: integral of cos1001 xsin5 xdx

A: Solution is given below..

Q: Evaluate the following integral: S² S²₂ S²x + yz dædydz 2y

A:

Q: dx (2x + 3)(1–x) 1. a) Integral Number in the attached Table: b) Values of the constants: a = b = c)…

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Q: Evaluate the integral: LIVE 1 I√9r²+25 dr.

A: We will solve the given question using simple Integration rules.

Q: 1 Evaluate the integral: S√72+6 dx O 2√7x+6+C O 7 2√7x+6 +C ○ // √√7x + 6 + C 1 0- + C 3 7(7x+6) 2

A: use substitution method for solving the integral.