Question

$\int_{}^{}\frac{\sin^{4}x}{\cos^{8}x}$ dx is equal to –

• A. $\frac{(1 + \tan^{5}x)}{5} + \frac{\tan^{5}x}{7}$ + C
• B. $\frac{\tan^{5}x}{5} + \frac{\tan^{7}x}{7} + C$
• C. $\frac{\tan^{7}x}{5} + \frac{\tan^{5}x}{7}$ + C
• D. None of these

Answer 1

Answer: (B)

$\frac{\tan^{5}x}{5} + \frac{\tan^{7}x}{7} + C$

Answer 2

$\int \frac { \frac { \sin ^ { 4 } x } { \cos ^ { 4 } x } } { \frac { \cos ^ { 8 } x } { \cos ^ { 4 } x } }$ .dx = ̣ tan⁴x. sec⁴x dx

= ̣ tan⁴ x (1 + tan²x)sec²x dx = ̣ tan⁴x.

(1 + tan²x) d(tanx) = ̣ t⁴(1 + t²)= $\frac { \mathrm { t } ^ { 5 } } { 5 }$ + $\frac { \mathrm { t } ^ { 7 } } { 7 }$ + C