What is the integral of 1/(x^2+11) ?

The integral of 1/(x^2+11) is 1/(sqrt(11))arctan(x/(sqrt(11)))+C

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integral of 1/(x^2+11)

\int \frac{1}{x ^{2} + 11} d x

\frac{1}{11} arctan (\frac{x}{11}) + C

Solution steps

\int \frac{1}{x ^{2} + 11} d x

Apply Integral Substitution

= \int \frac{1}{11 ( 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}{11} \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}{11} arctan (u)

Substitute back

u = \frac{x}{11}

= \frac{1}{11} arctan (\frac{x}{11})

Add a constant to the solution

= \frac{1}{11} arctan (\frac{x}{11}) + C

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What is the integral of 1/(x^2+11) ?
The integral of 1/(x^2+11) is 1/(sqrt(11))arctan(x/(sqrt(11)))+C