What is the integral of 1/(3^2+x^2) ?

The integral of 1/(3^2+x^2) is 1/3 arctan(x/3)+C

Popular >

integral of 1/(3^2+x^2)

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

\frac{1}{3} arctan (\frac{x}{3}) + C

Solution steps

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

Apply Integral Substitution

= \int \frac{1}{3 ( u ^{2} + 1 )} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= \frac{1}{3} arctan (u)

Substitute back

u = \frac{x}{3}

= \frac{1}{3} arctan (\frac{x}{3})

Add a constant to the solution

= \frac{1}{3} arctan (\frac{x}{3}) + C

\int \frac{3 x + 2}{x ( x + 2 ) ^{2} + 16 x} d x

\int \frac{3}{[ x ( x + 3 ) ]} d x

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

\int sin^{2} (5 x) \cdot cos^{3} (5 x) d x

\int x (3 x + 4) d x

What is the integral of 1/(3^2+x^2) ?
The integral of 1/(3^2+x^2) is 1/3 arctan(x/3)+C