What is the integral of 1/((2\times 2+1)sqrt(x^2+1)) ?

The integral of 1/((2\times 2+1)sqrt(x^2+1)) is 1/5 ln|sqrt(x^2+1)+x|+C

Popular >

integral of 1/((2\times 2+1)sqrt(x^2+1))

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

\frac{1}{5} ln x^{2} + 1 + x + C

Solution steps

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

Take the constant out:

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

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

Simplify

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

Use the common integral:

\int \frac{1}{x ^{2} + 1} d x = ln x^{2} + 1 + x

= \frac{1}{5} ln x^{2} + 1 + x

Add a constant to the solution

= \frac{1}{5} ln x^{2} + 1 + x + C

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

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{16}} d x

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

\int \frac{sin ( x ) + sec ( x )}{tan ( x )} d x

\int (4 x + 2)^{3} d x

What is the integral of 1/((2\times 2+1)sqrt(x^2+1)) ?
The integral of 1/((2\times 2+1)sqrt(x^2+1)) is 1/5 ln|sqrt(x^2+1)+x|+C