Find the Integral $\int \tan ^{3} x \sec ^{5} x d x$

Multiple Choice

Find the integral. $\int \tan ^{3} x \sec ^{5} x d x$

A) $\frac{1}{5} \sec ^{5} x-\frac{1}{3} \sec ^{3} x+C$
B) $\frac{1}{5} \sec ^{3} x+\frac{1}{3} \sec ^{3} x+C$
C) $\frac{1}{7} \sec ^{7} x-\frac{1}{5} \sec ^{3} x+C$
D) $\frac{1}{7} \sec ^{7} x+\frac{1}{5} \sec ^{3} x+C$