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

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

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

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

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

Solution steps

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

\frac{1}{3 + 3 x ^{2}} = \frac{1}{3} \frac{1}{1 + x ^{2}}

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

Add a constant to the solution

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

\int \frac{1}{x 25 + x ^{2}} d x

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