Question

Evaluate: $\int {\tan }^{7}xdx+\int {\tan }^{9}xdx$

• A. $\frac{{\tan }^{7}x}{7}+c$
• B. ${\tan }^{7}x+c$
• C. $\frac{{\tan }^{10}x}{10}+c$
• D. $\frac{{\tan }^{8}x}{8}+c$

Answer 1

The correct option is D $\frac{{\tan }^{8}x}{8}+c$

$\int {\tan }^{7}x.dx+\int {\tan }^{9}x.dx$
$\int {\tan }^{7}x(1+{\tan }^{2}x).dx$
$\int {\tan }^{7}x{\sec }^{2}x.dx$
$\int {\tan }^{7}x.d\left(\tan x\right)$
$=\frac{{\tan }^{8}x}{8}+c$