What is the integral from 0 to 5 of xsqrt(1+x) ?

The integral from 0 to 5 of xsqrt(1+x) is 2/3+(72sqrt(6)-2)/5-4sqrt(6)

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integral from 0 to 5 of xsqrt(1+x)

\int_{0}^{5} x 1 + x d x

\frac{2}{3} + \frac{72 6 - 2}{5} - 46

Decimal Notation

25.74135 \dots

Solution steps

\int_{0}^{5} x 1 + x d x

Apply u-substitution

: \int_{1}^{6} (u - 1) u d u

= \int_{1}^{6} (u - 1) u d u

Expand

(u - 1) u : u^{\frac{3}{2}} - u

= \int_{1}^{6} u^{\frac{3}{2}} - u 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

= \int_{1}^{6} u^{\frac{3}{2}} d u - \int_{1}^{6} u d u

\int_{1}^{6} u^{\frac{3}{2}} d u = \frac{72 6 - 2}{5}

\int_{1}^{6} u d u = 46 - \frac{2}{3}

= \frac{72 6 - 2}{5} - (46 - \frac{2}{3})

Simplify

= \frac{2}{3} + \frac{72 6 - 2}{5} - 46

e^{x^{3} + 2 x}

\int \frac{7 + x + x ^{2}}{x} d x

f (x) = 8 x^{2} - x

\frac{d}{d x} (sin (\frac{π}{x}))

\frac{\partial}{\partial x} (ln (x^{3} + y^{7}))

What is the integral from 0 to 5 of xsqrt(1+x) ?
The integral from 0 to 5 of xsqrt(1+x) is 2/3+(72sqrt(6)-2)/5-4sqrt(6)