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

The integral from 3 to 7 of x/(sqrt(7+x^2)) is 2(sqrt(14)-2)

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

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

2 (14 - 2)

Decimal

3.48331 \dots

Solution steps

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

Apply u-substitution

= \int_{16}^{56} \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_{16}^{56} \frac{1}{u} d u

Apply the Power Rule

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{16}^{56}

Apply radical rule:

= \frac{1}{2} [2 u]_{16}^{56}

Compute the boundaries:

414 - 8

= \frac{1}{2} (414 - 8)

Simplify

= 2 (14 - 2)

What is the integral from 3 to 7 of x/(sqrt(7+x^2)) ?
The integral from 3 to 7 of x/(sqrt(7+x^2)) is 2(sqrt(14)-2)