What is the integral of 3/(4x^2+4) ?

The integral of 3/(4x^2+4) is 3/4 arctan(x)+C

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integral of 3/(4x^2+4)

\int \frac{3}{4 x ^{2} + 4} d x

\frac{3}{4} arctan (x) + C

Solution steps

\int \frac{3}{4 x ^{2} + 4} 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}{4 x ^{2} + 4} d x

\frac{1}{4 x ^{2} + 4} = \frac{1}{4} \frac{1}{x ^{2} + 1}

= 3 \cdot \int \frac{1}{4} \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}{4} \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}{4} arctan (x)

Simplify

3 \cdot \frac{1}{4} arctan (x) : \frac{3}{4} arctan (x)

= \frac{3}{4} arctan (x)

Add a constant to the solution

= \frac{3}{4} arctan (x) + C

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What is the integral of 3/(4x^2+4) ?
The integral of 3/(4x^2+4) is 3/4 arctan(x)+C