Evaluate the following integrals : `int{3sinx-4cosx+5/(cos^2x)-6/(sin^2x)+tan^2x-cot^2x}dx`

Explanation

`int(3 sin x-4 cos x+frac{5}{cos ^{2} x}-frac{6}{sin ^{2} x}+tan ^{2} x-cot ^{2} x) d x `
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=3 sin x d x-4 cos x d x+int frac{5 d x}{cos ^{2} x}-int frac{6}{sin ^{2} x} d x+int tan ^{2} x d x-int cot ^{2} x d x `
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=3 sin x d x-4 cos x d x+5 int frac{d x}{cos ^{2} x}-6 int frac{d x}{sin ^{2} x}+int tan ^{2} x d x-int cot ^{2} x d x `
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=3 sin x d x-4 cos x d x+5 int sec ^{2} x d x-6 int csc ^{2} x d x+int sec ^{2} x d x-int d x-
int csc 2 x d x+int d x `
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=3 sin x d x-4 cos x d x+5 int sec ^{2} x d x-6 int csc ^{2} x d x+int sec ^{2} x d x-int csc ^{2} x d x `
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=3(-cos x)-4 sin x+5 tan x+6 cot x+tan ^{2} x+cot x+c`
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