What is the integral of (6/(5+5x^2)) ?

The integral of (6/(5+5x^2)) is 6/5 arctan(x)+C

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integral of (6/(5+5x^2))

\int (\frac{6}{5 + 5 x ^{2}}) d x

\frac{6}{5} arctan (x) + C

Solution steps

\int \frac{6}{5 + 5 x ^{2}} d x

Take the constant out:

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

= 6 \cdot \int \frac{1}{5 + 5 x ^{2}} d x

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

= 6 \cdot \int \frac{1}{5} \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

= 6 \cdot \frac{1}{5} \cdot \int \frac{1}{1 + x ^{2}} d x

Use the common integral:

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

= 6 \cdot \frac{1}{5} arctan (x)

Simplify

6 \cdot \frac{1}{5} arctan (x) : \frac{6}{5} arctan (x)

= \frac{6}{5} arctan (x)

Add a constant to the solution

= \frac{6}{5} arctan (x) + C

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What is the integral of (6/(5+5x^2)) ?
The integral of (6/(5+5x^2)) is 6/5 arctan(x)+C