What is the integral from 0 to 3 of x/(sqrt(x^2+1)) ?

The integral from 0 to 3 of x/(sqrt(x^2+1)) is sqrt(10)-1

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integral from 0 to 3 of x/(sqrt(x^2+1))

\int_{0}^{3} \frac{x}{x ^{2} + 1} d x

10 - 1

Solution steps

\int_{0}^{3} \frac{x}{x ^{2} + 1} d x

Apply u-substitution

: \int_{1}^{10} \frac{1}{2 u} d u

= \int_{1}^{10} \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_{1}^{10} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{1}^{10}

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{1}^{10}

Apply radical rule:

= \frac{1}{2} [2 u]_{1}^{10}

Compute the boundaries:

210 - 2

= \frac{1}{2} (210 - 2)

Simplify

= 10 - 1

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What is the integral from 0 to 3 of x/(sqrt(x^2+1)) ?
The integral from 0 to 3 of x/(sqrt(x^2+1)) is sqrt(10)-1