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Evaluate the following integrals: (i)...

Evaluate the following integrals:
`(i) int 2x sqrt(1 + x^2)dx " " (ii) int e^(-x^2) x dx " " (iii) int (sin x)/(1 + cos x) dx`
`(iv) int 1/(1 + x^2)dx " " (v) int x (a - x)^8 dx`.

Text Solution

Verified by Experts

The correct Answer is:
(i) `2/3 (1 + x^2)^(3/2) + c`
(ii) `-1/2 e^(-x^2) + c`.
(iii) `-log |1 + cos x| + c`
(iv) `tan^(-1)x + c`
(v) `-(a(a - x)^9)/(9) + c`.
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