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

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

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

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

2 (23 - \frac{10}{3})

Decimal

0.26153 \dots

Solution steps

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

Apply u-substitution

: \int_{3}^{2} 2 (u^{2} - 3) d u

= \int_{3}^{2} 2 (u^{2} - 3) d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{3}^{2} u^{2} - 3 d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int_{3}^{2} u^{2} d u - \int_{3}^{2} 3 d u)

\int_{3}^{2} u^{2} d u = \frac{8}{3} - 3

\int_{3}^{2} 3 d u = 6 - 33

= 2 (\frac{8}{3} - 3 - (6 - 33))

Expand

\frac{8}{3} - 3 - (6 - 33) : 23 - \frac{10}{3}

= 2 (23 - \frac{10}{3})

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