What is the integral of 3/(5x^2+5) ?

The integral of 3/(5x^2+5) is 3/5 arctan(x)+C

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integral of 3/(5x^2+5)

\int \frac{3}{5 x ^{2} + 5} d x

\frac{3}{5} arctan (x) + C

Solution steps

\int \frac{3}{5 x ^{2} + 5} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{5 x ^{2} + 5} d x

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

= 3 \cdot \int \frac{1}{5} \cdot \frac{1}{x ^{2} + 1} d x

Take the constant out:

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

= 3 \cdot \frac{1}{5} \cdot \int \frac{1}{x ^{2} + 1} d x

Use the common integral:

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

= 3 \cdot \frac{1}{5} arctan (x)

Simplify

3 \cdot \frac{1}{5} arctan (x) : \frac{3}{5} arctan (x)

= \frac{3}{5} arctan (x)

Add a constant to the solution

= \frac{3}{5} arctan (x) + C

(9 x + 0.8 x^{2} + 0.07 x^{3})^{^{'}}

y = cos (x)

ln (\frac{1 + x}{1 - x})

\frac{d}{d x} (lo g_{5} (4 x^{2} + 5 x - 8))

What is the integral of 3/(5x^2+5) ?
The integral of 3/(5x^2+5) is 3/5 arctan(x)+C