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Popular >

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

Solution

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

Solution

\frac{arctan ^{2} ( x )}{2} + C

Solution steps

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

Simplify

arctan (x) \frac{1}{1 + x ^{2}} : \frac{arctan ( x )}{1 + x ^{2}}

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = arctan (x)

= \frac{arctan ^{2} ( x )}{2}

Add a constant to the solution

= \frac{arctan ^{2} ( x )}{2} + C

Popular Examples

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\int sin^{2} (\frac{x}{5}) cos (\frac{x}{5}) d x

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

\int \frac{5 x}{( x - 1 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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