What is the integral of 1/(u^2+a^2) ?

The integral of 1/(u^2+a^2) is 1/a arctan(u/a)+C

Popular >

integral of 1/(u^2+a^2)

\int \frac{1}{u ^{2} + a ^{2}} d u

\frac{1}{a} arctan (\frac{u}{a}) + C

Solution steps

\int \frac{1}{u ^{2} + a ^{2}} d u

Apply Integral Substitution

= \int \frac{1}{a ( 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}{a} \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}{a} arctan (v)

Substitute back

v = \frac{u}{a}

= \frac{1}{a} arctan (\frac{u}{a})

Add a constant to the solution

= \frac{1}{a} arctan (\frac{u}{a}) + C

n = 1 \sum \infty \frac{1}{n ( n + 2 )}

1 - 4 x

n = 1 \sum \infty \frac{( 1 )}{n ^{2}}

\frac{d ^{2}}{d x ^{2}} (ln (1 + e^{x}))

\frac{\partial}{\partial x} (7 x + 8 y^{2})

What is the integral of 1/(u^2+a^2) ?
The integral of 1/(u^2+a^2) is 1/a arctan(u/a)+C