Solve the following integrals: i. - 3 d: x² +9 ii. (x² – 1 {x* + 4}** -1\x² +4)*

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A: We have to calculate this definite integral which is given by

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A: The integration of the integral is 1/[x2(9x2-4)3/2].

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A: I = ∫x2+152x8dxI = ?

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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…

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A: Let's find.

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A: Our Aim is to evaluate the integral given below:-I=∫xe2x(1+2x)2dx  -(i)

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A: we have to evaluate the following integral . First we decompose into partial fraction then we can…

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A: Given