What is the integral of sin^2(x)+sec^2(5x) ?

The integral of sin^2(x)+sec^2(5x) is 1/2 (x-1/2 sin(2x))+1/5 tan(5x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin^2(x)+sec^2(5x)

\int sin^{2} (x) + sec^{2} (5 x) d x

\frac{1}{2} (x - \frac{1}{2} sin (2 x)) + \frac{1}{5} tan (5 x) + C

Solution steps

\int sin^{2} (x) + sec^{2} (5 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin^{2} (x) d x + \int sec^{2} (5 x) d x

\int sin^{2} (x) d x = \frac{1}{2} (x - \frac{1}{2} sin (2 x))

\int sec^{2} (5 x) d x = \frac{1}{5} tan (5 x)

= \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + \frac{1}{5} tan (5 x)

Add a constant to the solution

= \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + \frac{1}{5} tan (5 x) + C

\int x 36 - x^{4} d x

\int 5 sin^{5} (x) cos^{4} (x) d x

\int x^{5} e^{5 x} d x

\int ln^{2} (\frac{4}{x}) d x

\int 8 x - 3 x d x

What is the integral of sin^2(x)+sec^2(5x) ?
The integral of sin^2(x)+sec^2(5x) is 1/2 (x-1/2 sin(2x))+1/5 tan(5x)+C