What is the integral from-0 to+5 of x/(sqrt(4+x^2)) ?

The integral from-0 to+5 of x/(sqrt(4+x^2)) is sqrt(29)-2

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integral from-0 to+5 of x/(sqrt(4+x^2))

\int_{- 0}^{+ 5} \frac{x}{4 + x ^{2}} d x

29 - 2

Decimal Notation

3.38516 \dots

Solution steps

\int_{- 0}^{5} \frac{x}{4 + x ^{2}} d x

Apply u-substitution

: \int_{4}^{29} \frac{1}{2 u} d u

= \int_{4}^{29} \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_{4}^{29} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{4}^{29}

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{4}^{29}

Apply radical rule:

= \frac{1}{2} [2 u]_{4}^{29}

Compute the boundaries:

229 - 4

= \frac{1}{2} (229 - 4)

Simplify

= 29 - 2

\int_{- 1}^{1} 4 x^{2} + 1 d x

\int_{- 3}^{3} \frac{1}{( x + 2 ) ^{3}} d x

\int_{- 1}^{3} 3 - 2 x d x

\int_{- 1}^{2} \frac{1}{3} x^{3} d x

\int_{0}^{3} k x^{2} + \frac{1}{30} d x

What is the integral from-0 to+5 of x/(sqrt(4+x^2)) ?
The integral from-0 to+5 of x/(sqrt(4+x^2)) is sqrt(29)-2