What is the integral from 0 to 1 of x^4(5+3x^5)^4 ?

The integral from 0 to 1 of x^4(5+3x^5)^4 is 9881/25

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integral from 0 to 1 of x^4(5+3x^5)^4

\int_{0}^{1} x^{4} (5 + 3 x^{5})^{4} d x

\frac{9881}{25}

Decimal

395.24

Solution steps

\int_{0}^{1} x^{4} (5 + 3 x^{5})^{4} d x

Expand

x^{4} (5 + 3 x^{5})^{4} : 625 x^{4} + 1500 x^{9} + 1350 x^{14} + 540 x^{19} + 81 x^{24}

= \int_{0}^{1} 625 x^{4} + 1500 x^{9} + 1350 x^{14} + 540 x^{19} + 81 x^{24} 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} 625 x^{4} d x + \int_{0}^{1} 1500 x^{9} d x + \int_{0}^{1} 1350 x^{14} d x + \int_{0}^{1} 540 x^{19} d x + \int_{0}^{1} 81 x^{24} d x

\int_{0}^{1} 625 x^{4} d x = 125

\int_{0}^{1} 1500 x^{9} d x = 150

\int_{0}^{1} 1350 x^{14} d x = 90

\int_{0}^{1} 540 x^{19} d x = 27

\int_{0}^{1} 81 x^{24} d x = \frac{81}{25}

= 125 + 150 + 90 + 27 + \frac{81}{25}

Simplify

125 + 150 + 90 + 27 + \frac{81}{25} : \frac{9881}{25}

= \frac{9881}{25}

\int_{0}^{1} - 1 - x^{2} d x

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\int_{0}^{3} x^{2} e^{x} d x

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

What is the integral from 0 to 1 of x^4(5+3x^5)^4 ?
The integral from 0 to 1 of x^4(5+3x^5)^4 is 9881/25