Question

integral of
3+ 4 sin 5x/
cos²5x dx​

Answer 1

Step-by-step explanation:

We have,

$\int \frac{3 + 4 \sin(5x) }{ \cos ^{2} (5x) } dx$

$= \int \frac{3}{ \cos ^{2} (5x) } dx + \int 4\frac{ \sin(5x) }{ \cos^{2} (5x) } dx$

$= 3 \int \sec^{2} (5x) dx + 4 \int \tan(5x) \sec(5x) dx$

$= 3 \times \frac{ \tan(5x) }{5} + 4 \times \frac{ \sec(5x) }{5} + c$

$= \frac{3}{5} \tan(5x) + \frac{4}{5} \sec(5x) + c$