Question

$\int_{}^{}\sqrt[3]{\frac{\sin^{n}x}{\cos^{n + 6}x}}$dx, n Ī N is equal to –

• A. $\frac{3}{n}(\tan x)^{\frac{n}{3} + 1} + c$
• B. $\frac{3}{3 + n}(\tan x)^{\frac{n}{3} + 1} + c$
• C. $\frac{3}{n}(\cos x)^{n + 1} + c$
• D. None of these

Answer 1

Answer: (B)

$\frac{3}{3 + n}(\tan x)^{\frac{n}{3} + 1} + c$

Answer 2

$\int \sqrt [ 3 ] { \frac { \sin ^ { n } x } { \cos ^ { n + 6 } x } }$ dx = dx

=

= (tan x)

= + c

= + c.

Hence (2) is the correct answer.