What is the integral from-10 to 10 of (10)/(x^2+25) ?

The integral from-10 to 10 of (10)/(x^2+25) is 4arctan(2)

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integral from-10 to 10 of (10)/(x^2+25)

\int_{- 10}^{10} \frac{10}{x ^{2} + 25} d x

4 arctan (2)

Decimal Notation

4.42859 \dots

Solution steps

\int_{- 10}^{10} \frac{10}{x ^{2} + 25} d x

Take the constant out:

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

= 10 \cdot \int_{- 10}^{10} \frac{1}{x ^{2} + 25} d x

Apply Integral Substitution

= 10 \cdot \int_{- 2}^{2} \frac{1}{5 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 10 \cdot \frac{1}{5} \cdot \int_{- 2}^{2} \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 10 \cdot \frac{1}{5} [arctan (u)]_{- 2}^{2}

Simplify

10 \cdot \frac{1}{5} [arctan (u)]_{- 2}^{2} : 2 [arctan (u)]_{- 2}^{2}

= 2 [arctan (u)]_{- 2}^{2}

Compute the boundaries:

2 arctan (2)

= 2 \cdot 2 arctan (2)

Simplify

= 4 arctan (2)

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What is the integral from-10 to 10 of (10)/(x^2+25) ?
The integral from-10 to 10 of (10)/(x^2+25) is 4arctan(2)