Evaluate ∫ (3 sin x-2 cos x+4 sec2 x-5 cos ec2x)dx

Question

Evaluate ∫ (3 sin x-2 cos x+4 sec2 x-5 cos ec2x)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

Tardigrade Admin · Accepted Answer

We have, I =∫ (3 sin x-2 cos x+4 sec2 x-5 cosec2x)dx ⇒ I=3 ∫ sin x dx — 2 ∫ cos x dx + 4 ∫ sec2x dx -5 ∫ cosec2x dx ⇒ I = -3 cos x - 2 sin x + 4 tan x + 5 cot x+ C

Q. Evaluate $\int (3 s in x - 2 cos x + 4 se c^{2} x - 5 cos e c^{2} x) d x$

$- 3 cos x - 2 s in x + 4 t an x + 5 co t x + C$

$3 cos x + 2 s in x + 4 t an x + 5 co t x + C$

$3 cos x + 2 s in x - 4 t an x - 5 co t x + C$

$- 3 cos x - 2 s in x - 4 t an x - 5 co t x + C$

We have,

$I = \int (3 s in x - 2 cos x + 4 se c^{2} x - 5 cose c^{2} x) d x$

$\Rightarrow I = 3 \int s in x d x —2 \int cos x d x + 4 \int se c^{2} x d x - 5 \int cose c^{2} x d x$

$\Rightarrow I = - 3 cos x - 2 s in x + 4 t an x + 5 co t x + C$

Q. Evaluate ∫(3sinx−2cosx+4sec2x−5cosec2x)dx

−3cosx−2sinx+4tanx+5cotx+C

3cosx+2sinx+4tanx+5cotx+C

3cosx+2sinx−4tanx−5cotx+C

−3cosx−2sinx−4tanx−5cotx+C