What is the integral from 0 to 1 of 5/(x^2+1) ?

The integral from 0 to 1 of 5/(x^2+1) is (5pi)/4

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integral from 0 to 1 of 5/(x^2+1)

\int_{0}^{1} \frac{5}{x ^{2} + 1} d x

\frac{5 π}{4}

Decimal

3.92699 \dots

Solution steps

\int_{0}^{1} \frac{5}{x ^{2} + 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{0}^{1} \frac{1}{x ^{2} + 1} d x

Use the common integral:

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

= 5 [arctan (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= 5 \cdot \frac{π}{4}

Simplify

= \frac{5 π}{4}

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

a re a x^{2}, 12 - x, [- 3, 4]

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

\frac{d}{d x} (c^{1} cos (x) + c^{2} sin (x))

x \to - 4 lim (12 x + 1)

What is the integral from 0 to 1 of 5/(x^2+1) ?
The integral from 0 to 1 of 5/(x^2+1) is (5pi)/4