What is the integral from 0 to 3 of x/(sqrt(x^2+7)) ?

The integral from 0 to 3 of x/(sqrt(x^2+7)) is 4-sqrt(7)

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integral from 0 to 3 of x/(sqrt(x^2+7))

\int_{0}^{3} \frac{x}{x ^{2} + 7} d x

4 - 7

Decimal

1.35424 \dots

Solution steps

\int_{0}^{3} \frac{x}{x ^{2} + 7} d x

Apply u-substitution

= \int_{7}^{16} \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_{7}^{16} \frac{1}{u} d u

Apply the Power Rule

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{7}^{16}

Apply radical rule:

= \frac{1}{2} [2 u]_{7}^{16}

Compute the boundaries:

8 - 27

= \frac{1}{2} (8 - 27)

Simplify

= 4 - 7

What is the integral from 0 to 3 of x/(sqrt(x^2+7)) ?
The integral from 0 to 3 of x/(sqrt(x^2+7)) is 4-sqrt(7)