What is the integral of (sec^2(x))/(sqrt(1+2tan(x))) ?

The integral of (sec^2(x))/(sqrt(1+2tan(x))) is sqrt(1+2tan(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sec^2(x))/(sqrt(1+2tan(x)))

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

1 + 2 tan (x) + C

Solution steps

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

Apply u-substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = 1 + 2 tan (x)

= 1 \cdot 1 + 2 tan (x)

Simplify

= 1 + 2 tan (x)

Add a constant to the solution

= 1 + 2 tan (x) + C

\int \frac{( 3 x ^{2} - 2 )}{x ( x + 1 ) ^{3}} d x

\int (5 x^{4} + 64) arctan (\frac{x}{2}) d x

f (x) = 5 - x

lo g_{10} (\frac{( x + 1 ) ( x - 8 )}{( x - 1 ) ( x + 8 )})

n = 1 \sum \infty \frac{1}{5 ^{n + 1}}

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