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

The integral from 1 to 4 of sqrt(x)(2+x) is 326/15

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

\int_{1}^{4} x (2 + x) d x

\frac{326}{15}

Decimal Notation

21.73333 \dots

Solution steps

\int_{1}^{4} x (2 + x) d x

Expand

x (2 + x) : 2 x + x^{\frac{3}{2}}

= \int_{1}^{4} 2 x + x^{\frac{3}{2}} d x

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}^{4} 2 x d x + \int_{1}^{4} x^{\frac{3}{2}} d x

\int_{1}^{4} 2 x d x = \frac{28}{3}

\int_{1}^{4} x^{\frac{3}{2}} d x = \frac{62}{5}

= \frac{28}{3} + \frac{62}{5}

Simplify

\frac{28}{3} + \frac{62}{5} : \frac{326}{15}

= \frac{326}{15}

w \to 0 lim (\frac{w ^{2}}{cos ( w ) - 1})

2 n d e^{2 e^{x}}

n = 1 \sum \infty \frac{n ^{2}}{3}

(3) (6.9)

\frac{d}{d x} ((x + 6)^{2})

What is the integral from 1 to 4 of sqrt(x)(2+x) ?
The integral from 1 to 4 of sqrt(x)(2+x) is 326/15