Question

Evaluate $\int \left(3\,sin\,x-2\,cos\,x+4\,sec^{2} \,x-5\,cos\,ec^{2}x\right)dx $

• A. $-3 \,cosx - 2 \,sinx + 4\, tanx + 5 cot\,x + C$
• B. $ 3 \,cosx + 2 \,sinx + 4 \,tanx + 5 \,cotx + C $
• C. $3 \,cosx + 2 \,sinx - 4\, tanx - 5 \,cotx + C$
• D. $- 3 \,cosx - 2 \,sinx - 4 \,tanx - 5 \,cotx + C $

Answer 1

Answer: (A)

We have,

$ I =\int \left(3\,sin\,x-2\,cos\,x+4\,sec^{2} x-5\,cosec^{2}x\right)dx$

$\Rightarrow I=3 \int sin\,x \,dx — 2 \int cos\,x dx + 4 \int sec^{2}x \,dx -5 \int cosec^{2}x dx$

$\Rightarrow I = -3 cos\,x - 2\,sin \,x + 4 tan\, x + 5 cot x+ C $