Find the indefinite integral. $$\int \tan ^ { 3 } 9 x d x$$
A) $\frac { 1 } { 18 } \tan ^ { 2 } 9 x - \frac { 1 } { 9 } \ln | \cos 9 x | + C$
B) $\frac { 1 } { 9 } \ln | \cos 9 x | + \frac { 1 } { 18 } \tan ^ { 2 } 9 x \sec 9 x + C$
C) $\frac { 1 } { 9 } \ln | \cos 9 x | + \frac { 1 } { 18 } \tan ^ { 2 } 9 x + C$
D) $\frac { 1 } { 9 } \ln | \cos 9 x | - \frac { 1 } { 18 } \sec ^ { 2 } 9 x + C$
E) $\frac { 1 } { 9 } \ln | \cos 9 x | + \frac { 1 } { 18 } \sec ^ { 2 } 9 x + C$

Question

Quizplus · Accepted Answer

Integration by parts with $u = \tan^2 9x$ and $dv = \tan 9x dx$ gives$$\int \tan^3 9x dx = \frac{1}{9} \tan^2 9x - \frac{1}{9} \ln |\cos 9x| + C.$$

Find the Indefinite Integral ∫tan⁡39xdx\int \tan ^ { 3 } 9 x d x∫tan39xdx

Find the Indefinite Integral $\int \tan ^ { 3 } 9 x d x$