What is the integral of (1/(7+7x^2)) ?

The integral of (1/(7+7x^2)) is 1/7 arctan(x)+C

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integral of (1/(7+7x^2))

\int (\frac{1}{7 + 7 x ^{2}}) d x

\frac{1}{7} arctan (x) + C

Solution steps

\int \frac{1}{7 + 7 x ^{2}} d x

\frac{1}{7 + 7 x ^{2}} = \frac{1}{7} \frac{1}{1 + x ^{2}}

= \int \frac{1}{7} \cdot \frac{1}{1 + x ^{2}} d x

Take the constant out:

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

= \frac{1}{7} \cdot \int \frac{1}{1 + x ^{2}} d x

Use the common integral:

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

= \frac{1}{7} arctan (x)

Add a constant to the solution

= \frac{1}{7} arctan (x) + C

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What is the integral of (1/(7+7x^2)) ?
The integral of (1/(7+7x^2)) is 1/7 arctan(x)+C