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Popular >

integral from 0 to 1 of arctan(4x)

Solution

\int_{0}^{1} arctan (4 x) d x

Solution

arctan (4) - \frac{1}{8} ln (17)

+1

Decimal Notation

0.97166 \dots

Solution steps

\int_{0}^{1} arctan (4 x) d x

Apply Integration By Parts

: [x arctan (4 x) - \int \frac{4 x}{16 x ^{2} + 1} d x]_{0}^{1}

= [x arctan (4 x) - \int \frac{4 x}{16 x ^{2} + 1} d x]_{0}^{1}

\int \frac{4 x}{16 x ^{2} + 1} d x = \frac{1}{8} ln 16 x^{2} + 1

= [x arctan (4 x) - \frac{1}{8} ln 16 x^{2} + 1]_{0}^{1}

Compute the boundaries:

arctan (4) - \frac{1}{8} ln (17)

= arctan (4) - \frac{1}{8} ln (17)

Popular Examples

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

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\int sin (\frac{nπ x}{5}) d x

y^{^{'}} = \frac{1}{x} y

limit as x approaches 0-of e^{1/x}

x \to 0 - lim (e^{\frac{1}{x}})

integral of (sqrt(36x^2-1))/x

\int \frac{36 x ^{2} - 1}{x} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of arctan(4x) ?
The integral from 0 to 1 of arctan(4x) is arctan(4)-1/8 ln(17)