What is the integral from 1 to 2 of x/(sqrt(x^2+4)) ?

The integral from 1 to 2 of x/(sqrt(x^2+4)) is 2sqrt(2)-sqrt(5)

Popular >

integral from 1 to 2 of x/(sqrt(x^2+4))

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

22 - 5

Solution steps

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

Apply u-substitution

: \int_{5}^{8} \frac{1}{2 u} d u

= \int_{5}^{8} \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_{5}^{8} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{5}^{8}

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{5}^{8}

Apply radical rule:

= \frac{1}{2} [2 u]_{5}^{8}

Compute the boundaries:

42 - 25

= \frac{1}{2} (42 - 25)

Simplify

= 22 - 5

\int_{- π}^{π} x sin (x) cos (n x) d x

\int_{1}^{8} 8 x^{\frac{1}{3}} d x

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

\int_{2}^{6} 2 d x

\int_{- 2 π}^{2 π} 8 sin (x) d x

What is the integral from 1 to 2 of x/(sqrt(x^2+4)) ?
The integral from 1 to 2 of x/(sqrt(x^2+4)) is 2sqrt(2)-sqrt(5)