Question

$\int \frac{{\sin }^{25}x}{{\cos }^{27}x}dx$ is equal to

• A. $\frac{{\sin }^{26}(x)}{26}+C$
• B. $\frac{{\cos }^{26}(x)}{26}+C$
• C. ${\tan }^{26}(x)+C$
• D. $\frac{{\tan }^{26}(x)}{26}+C$
• E. $26{\tan }^{26}(x)+C$

Answer 1

Answer: (D)

$\int {\tan }^{25}x\cdot {\sec }^{2}xdx$
$\tan x=t$
${\sec }^{2}xdx=dt$
$\int t^{25}dt=\frac{t^{26}}{26}+c$
$=\frac{{\tan }^{26}(x)}{26}+c$