What is the integral from 0 to 1 of sqrt(x)(1+2x^5) ?

The integral from 0 to 1 of sqrt(x)(1+2x^5) is 38/39

Popular >

integral from 0 to 1 of sqrt(x)(1+2x^5)

\int_{0}^{1} x (1 + 2 x^{5}) d x

\frac{38}{39}

Decimal Notation

0.97435 \dots

Solution steps

\int_{0}^{1} x (1 + 2 x^{5}) d x

Expand

x (1 + 2 x^{5}) : x + 2 x^{\frac{11}{2}}

= \int_{0}^{1} x + 2 x^{\frac{11}{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_{0}^{1} x d x + \int_{0}^{1} 2 x^{\frac{11}{2}} d x

\int_{0}^{1} x d x = \frac{2}{3}

\int_{0}^{1} 2 x^{\frac{11}{2}} d x = \frac{4}{13}

= \frac{2}{3} + \frac{4}{13}

Simplify

\frac{2}{3} + \frac{4}{13} : \frac{38}{39}

= \frac{38}{39}

\int_{1}^{2} \frac{- 9 ln ( x )}{x ^{2}} d x

\int \frac{x + 2}{x - 3} d x

\int (\frac{5 x ^{2} + x - 4}{x ^{2}}) d x

y = - 2 t^{3}, (- 1, 2)

\frac{\partial}{\partial y} (\frac{3 x y}{x ^{4} + y ^{4}})

What is the integral from 0 to 1 of sqrt(x)(1+2x^5) ?
The integral from 0 to 1 of sqrt(x)(1+2x^5) is 38/39