Evaluate the following integrals :∫{3sin x - 4cos x + 5/cos^2x - 6/sin^2x + tan^2x - cot^2x}dx ​

Question

Evaluate the following integrals : 

\(\int\)\(\{\)3sin x - 4cos x + \(\frac{5}{cos^2x}\) - \(\frac{6}{sin^2x}\) + tan²x - cot²x\(\}\)dx

Answer 1

Let I =\(\int\)\(\{\)3sin x - 4cos x + \(\frac{5}{cos^2x}\) - \(\frac{6}{sin^2x}\) + tan²x - cot²x\(\}\)dx

⇒ I = 3(–cos x) – 4(sin x) + 6(tan x) – 7(–cot x) + c 

∴ I = –3cosx – 4sinx + 6tanx + 7cotx + c

Thus,