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Evaluate: (i) int(5x^(2) + 2x^(-5) - 7...

Evaluate:
(i) `int(5x^(2) + 2x^(-5) - 7x + 1/(sqrt(x)) +5/x) dx`
(ii) `int(3sinx - 4 cosx + 5 sec^(2) x - 2cosec^(2)x) dx`
(iii) `int(1-x)(2+3x)(5-4x)dx`
(iv) `int((3x^(4) - 5x^(3) + 4x^(2) -x + 2)/(x^(3)))dx` , (v) `int(x^(2) + 1/(x^(2)))^(3) dx`

Text Solution

Verified by Experts

`int(3sinx-4cosx+5sec^(2)x-2cosec^(2)x)dx`
`=3intsinxdx-4intcosxdx+5intsec^(2)xdx-2intcosec^(2)xdx`
`=-3(cosx)-4sinx+5tanx+2(cotx)+C`
`=-3cosx-4sinx+5tanx+2cotx+C`
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