What is the integral from 0 to 7 of x/(sqrt(x^2+15)) ?

The integral from 0 to 7 of x/(sqrt(x^2+15)) is 8-sqrt(15)

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integral from 0 to 7 of x/(sqrt(x^2+15))

\int_{0}^{7} \frac{x}{x ^{2} + 15} d x

8 - 15

Decimal Notation

4.12701 \dots

Solution steps

\int_{0}^{7} \frac{x}{x ^{2} + 15} d x

Apply u-substitution

: \int_{15}^{64} \frac{1}{2 u} d u

= \int_{15}^{64} \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{15}^{64} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{15}^{64}

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{15}^{64}

Apply radical rule:

= \frac{1}{2} [2 u]_{15}^{64}

Compute the boundaries:

16 - 215

= \frac{1}{2} (16 - 215)

Simplify

= 8 - 15

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What is the integral from 0 to 7 of x/(sqrt(x^2+15)) ?
The integral from 0 to 7 of x/(sqrt(x^2+15)) is 8-sqrt(15)