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