What is the integral from 0 to x of arctan(x) ?

The integral from 0 to x of arctan(x) is xarctan(x)-1/2 ln|x^2+1|

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integral from 0 to x of arctan(x)

\int_{0}^{x} arctan (x) d x

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

Solution steps

\int_{0}^{x} arctan (x) d x

Apply Integration By Parts

: [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{0}^{x}

= [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{0}^{x}

\int \frac{x}{x ^{2} + 1} d x = \frac{1}{2} ln x^{2} + 1

= [x arctan (x) - \frac{1}{2} ln x^{2} + 1]_{0}^{x}

Compute the boundaries:

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

= x arctan (x) - \frac{1}{2} ln x^{2} + 1

\int_{0}^{5} (25 - x^{2}) d x

\int_{2}^{6} \frac{x}{x ^{2} - 3} d x

\int_{0}^{3} \frac{1}{x ^{2} + 1} d x

\int_{e^{- 1}}^{e^{1}} ∣ ln (x) ∣ d x

\int_{1}^{3} (1 + ln (x)) x^{x} d x

What is the integral from 0 to x of arctan(x) ?
The integral from 0 to x of arctan(x) is xarctan(x)-1/2 ln|x^2+1|