What is the integral of 1/(100x^2+1) ?

The integral of 1/(100x^2+1) is 1/10 arctan(10x)+C

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integral of 1/(100x^2+1)

\int \frac{1}{100 x ^{2} + 1} d x

\frac{1}{10} arctan (10 x) + C

Solution steps

\int \frac{1}{100 x ^{2} + 1} d x

Apply Integral Substitution

= \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

= \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)

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

Substitute back

u = 10 x

= \frac{1}{10} arctan (10 x)

Add a constant to the solution

= \frac{1}{10} arctan (10 x) + C

y^{^{'}} = \frac{y}{x} + \frac{6 x ^{3}}{y} cos (x^{2})

y = 2 x + x^{2}, (- 2, 0)

\int x \cdot x d x

y = (x^{2} - 7 x)^{2}

\frac{x}{x ^{2} + 100}

What is the integral of 1/(100x^2+1) ?
The integral of 1/(100x^2+1) is 1/10 arctan(10x)+C