What is the integral of 3/(2x^2+50) ?

The integral of 3/(2x^2+50) is 3/10 arctan(x/5)+C

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integral of 3/(2x^2+50)

\int \frac{3}{2 x ^{2} + 50} d x

\frac{3}{10} arctan (\frac{x}{5}) + C

Solution steps

\int \frac{3}{2 x ^{2} + 50} 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}{2 x ^{2} + 50} d x

Apply Integral Substitution

= 3 \cdot \int \frac{1}{10 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 3 \cdot \frac{1}{10} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 3 \cdot \frac{1}{10} arctan (u)

Substitute back

u = \frac{2}{5 2} x

= 3 \cdot \frac{1}{10} arctan (\frac{2}{5 2} x)

Simplify

3 \cdot \frac{1}{10} arctan (\frac{2}{5 2} x) : \frac{3}{10} arctan (\frac{x}{5})

= \frac{3}{10} arctan (\frac{x}{5})

Add a constant to the solution

= \frac{3}{10} arctan (\frac{x}{5}) + C

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

\int (3 x^{2} - 9)^{20} \cdot 2 x d x

\int 2 x + x^{2} d x

\int 4 x^{4} e^{2 x^{5}} d x

What is the integral of 3/(2x^2+50) ?
The integral of 3/(2x^2+50) is 3/10 arctan(x/5)+C