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

The integral from 1 to 3 of x(sqrt(x)+1) is (18sqrt(3)-2)/5+4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{18 3 - 2}{5} + 4

Decimal Notation

9.83538 \dots

Solution steps

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

Expand

x (x + 1) : x^{\frac{3}{2}} + x

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

\int_{1}^{3} x^{\frac{3}{2}} d x = \frac{18 3 - 2}{5}

\int_{1}^{3} x d x = 4

= \frac{18 3 - 2}{5} + 4

\int_{0}^{1} c x d x

\int_{0}^{2 π} 7 t 2 d t

\int_{0}^{\infty} 13 x e^{2 x} d x

\int_{0}^{7} \frac{1}{x ^{0.7}} d x

\int_{1}^{2} 5 x^{3} d x

What is the integral from 1 to 3 of x(sqrt(x)+1) ?
The integral from 1 to 3 of x(sqrt(x)+1) is (18sqrt(3)-2)/5+4