What is the integral from-2 to 3 of arctan(x) ?

The integral from-2 to 3 of arctan(x) is 3arctan(3)-2arctan(2)-(ln(2))/2

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integral from-2 to 3 of arctan(x)

\int_{- 2}^{3} arctan (x) d x

3 arctan (3) - 2 arctan (2) - \frac{ln ( 2 )}{2}

Decimal Notation

1.18626 \dots

Solution steps

\int_{- 2}^{3} arctan (x) d x

Apply Integration By Parts

: [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{- 2}^{3}

= [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{- 2}^{3}

\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]_{- 2}^{3}

Compute the boundaries:

3 arctan (3) - 2 arctan (2) + \frac{- ln ( 10 ) + ln ( 5 )}{2}

= 3 arctan (3) - 2 arctan (2) + \frac{- ln ( 10 ) + ln ( 5 )}{2}

Simplify

= 3 arctan (3) - 2 arctan (2) - \frac{ln ( 2 )}{2}

\int_{0}^{3} 9 e^{- 2 x} d x

\int_{x}^{y} 2^{l n (t)} d t

\int_{- 2}^{2} x^{2} + a x^{3} + b x^{4} d x

\int_{0.5}^{1} 1 d x

\int_{0}^{l n (2)} e^{2 x + 1} d x

What is the integral from-2 to 3 of arctan(x) ?
The integral from-2 to 3 of arctan(x) is 3arctan(3)-2arctan(2)-(ln(2))/2