∫ sin 3 x ( cos 4 x + 3 cos 2 x + 1 ) tan − 1 ( sec x + cos x ) d x = Options: A . &nbsp tan − 1 ( sec x + cos x ) + c B . &nbsp log | tan − 1 ( sec x + cos x ) | + c C . &nbsp 1 ( sec x + cos 2 x ) 2 + c D . &nbsp log | sec x + cos x | + c

Answer: Option B : B Put tan − 1 ( sec x + cos x ) = f ( x ) ⇒ f ′ ( x ) = sin 3 x cos 4 x + 3 cos 2 x + 1 ∴ ∫ f ′ ( x ) f ( x ) d x = log | f ( x ) | + c ∴ Integral = log | tan − 1 ( sec x + cos x ) | + c

∫sin3x(cos4x+3cos2x+1)tan−1(secx+cosx)dx=

Discussion Forum : Indefinite Integration

Question -

$\int \frac{{sin}^{3} x}{({cos}^{4} x + 3 {cos}^{2} x + 1) {tan}^{- 1} (sec x + cos x)} d x =$

Options:

A .

{tan}^{- 1} (sec x + cos x) + c

B .

log | {tan}^{- 1} (sec x + cos x) | + c

C .

\frac{1}{(sec x + {cos}^{2} x)^{2}} + c

D .

log | sec x + cos x | + c

Answer: Option B
:
B
Put

{tan}^{- 1} (sec x + cos x) = f (x) \Rightarrow f^{'} (x) = \frac{{sin}^{3} x}{{cos}^{4} x + 3 {cos}^{2} x + 1} ∴ \int \frac{f^{'} (x)}{f (x)} d x = log | f (x) | + c ∴ Integral = log | {tan}^{- 1} (sec x + cos x) | + c

Was this answer helpful ?

Next Question

Discussion Forum : Indefinite Integration

Submit Your Solution hear: