What is the integral of 1/(5+5x^2) ?

The integral of 1/(5+5x^2) is 1/5 arctan(x)+C

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integral of 1/(5+5x^2)

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

\frac{1}{5} arctan (x) + C

Solution steps

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

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

= \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

= \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)

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

Add a constant to the solution

= \frac{1}{5} arctan (x) + C

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

\int e^{t a n (10 x)} sec^{2} (10 x) d x

\int ln (- 2 x) d x

\int x^{2} - 3 x d x

\int \frac{5 x}{x} d x

What is the integral of 1/(5+5x^2) ?
The integral of 1/(5+5x^2) is 1/5 arctan(x)+C