What is the integral of 1/(sqrt(e^{2x)-25)} ?

The integral of 1/(sqrt(e^{2x)-25)} is 1/5 arctan((sqrt(e^{2x)-25})/5)+C

Popular >

integral of 1/(sqrt(e^{2x)-25)}

\int \frac{1}{e ^{2 x} - 25} d x

\frac{1}{5} arctan (\frac{e ^{2 x} - 25}{5}) + C

Solution steps

\int \frac{1}{e ^{2 x} - 25} d x

Apply u-substitution

: \int \frac{1}{u ^{2} + 25} d u

= \int \frac{1}{u ^{2} + 25} d u

Apply Integral Substitution

= \int \frac{1}{5 ( v ^{2} + 1 )} d v

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int \frac{1}{v ^{2} + 1} d v

Use the common integral:

\int \frac{1}{v ^{2} + 1} d v = arctan (v)

= \frac{1}{5} arctan (v)

Substitute back

= \frac{1}{5} arctan (\frac{e ^{2 x} - 25}{5})

Add a constant to the solution

= \frac{1}{5} arctan (\frac{e ^{2 x} - 25}{5}) + C

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

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

\int x (3 x^{2} + 2)^{8} d x

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

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

What is the integral of 1/(sqrt(e^{2x)-25)} ?
The integral of 1/(sqrt(e^{2x)-25)} is 1/5 arctan((sqrt(e^{2x)-25})/5)+C