What is the integral from 0 to 2 of x(2+x^5) ?

The integral from 0 to 2 of x(2+x^5) is 156/7

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integral from 0 to 2 of x(2+x^5)

\int_{0}^{2} x (2 + x^{5}) d x

\frac{156}{7}

Decimal

22.28571 \dots

Solution steps

\int_{0}^{2} x (2 + x^{5}) d x

Expand

x (2 + x^{5}) : 2 x + x^{6}

= \int_{0}^{2} 2 x + x^{6} 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_{0}^{2} 2 x d x + \int_{0}^{2} x^{6} d x

\int_{0}^{2} 2 x d x = 4

\int_{0}^{2} x^{6} d x = \frac{128}{7}

= 4 + \frac{128}{7}

Simplify

4 + \frac{128}{7} : \frac{156}{7}

= \frac{156}{7}

\frac{d}{d x} (\frac{2}{cos ( x ) cot ( x )})

\int \frac{5}{x + 6} d x

y = x - 4, y^{2} = 2 x

x \to + 0 lim (x ln (\frac{1}{x}))

(sin (x)) (sec (x))

What is the integral from 0 to 2 of x(2+x^5) ?
The integral from 0 to 2 of x(2+x^5) is 156/7