What is the integral from 1 to 5 of x(4+x^2)^{10} ?

The integral from 1 to 5 of x(4+x^2)^{10} is (29^{11}-48828125)/(22)

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integral from 1 to 5 of x(4+x^2)^{10}

\int_{1}^{5} x (4 + x^{2})^{10} d x

\frac{2 9 ^{11} - 48828125}{22}

Decimal

5.54569 E 14

Solution steps

\int_{1}^{5} x (4 + x^{2})^{10} d x

Apply u-substitution

: \int_{5}^{29} \frac{u ^{10}}{2} d u

= \int_{5}^{29} \frac{u ^{10}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{5}^{29} u^{10} d u

Apply the Power Rule

: [\frac{u ^{11}}{11}]_{5}^{29}

= \frac{1}{2} [\frac{u ^{11}}{11}]_{5}^{29}

Compute the boundaries:

\frac{2 9 ^{11}}{11} - \frac{48828125}{11}

= \frac{1}{2} (\frac{2 9 ^{11}}{11} - \frac{48828125}{11})

Simplify

= \frac{2 9 ^{11} - 48828125}{22}

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What is the integral from 1 to 5 of x(4+x^2)^{10} ?
The integral from 1 to 5 of x(4+x^2)^{10} is (29^{11}-48828125)/(22)