What is the integral from 0 to 1 of x^9(1+x^{10})^9 ?

The integral from 0 to 1 of x^9(1+x^{10})^9 is 1023/100

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integral from 0 to 1 of x^9(1+x^{10})^9

\int_{0}^{1} x^{9} (1 + x^{10})^{9} d x

\frac{1023}{100}

Decimal

10.23

Solution steps

\int_{0}^{1} x^{9} (1 + x^{10})^{9} d x

Apply u-substitution

: \int_{1}^{2} \frac{u ^{9}}{10} d u

= \int_{1}^{2} \frac{u ^{9}}{10} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{10} \cdot \int_{1}^{2} u^{9} d u

Apply the Power Rule

: [\frac{u ^{10}}{10}]_{1}^{2}

= \frac{1}{10} [\frac{u ^{10}}{10}]_{1}^{2}

Compute the boundaries:

\frac{1023}{10}

= \frac{1}{10} \cdot \frac{1023}{10}

Simplify

= \frac{1023}{100}

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What is the integral from 0 to 1 of x^9(1+x^{10})^9 ?
The integral from 0 to 1 of x^9(1+x^{10})^9 is 1023/100