What is the integral from-1 to 2 of 2x(x^2+1)^4 ?

The integral from-1 to 2 of 2x(x^2+1)^4 is 3093/5

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integral from-1 to 2 of 2x(x^2+1)^4

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

\frac{3093}{5}

Decimal Notation

618.6

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int_{2}^{5} \frac{u ^{4}}{2} d u

= 2 \cdot \int_{2}^{5} \frac{u ^{4}}{2} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int_{2}^{5} u^{4} d u

Apply the Power Rule

: [\frac{u ^{5}}{5}]_{2}^{5}

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

Simplify

2 \cdot \frac{1}{2} [\frac{u ^{5}}{5}]_{2}^{5} : [\frac{u ^{5}}{5}]_{2}^{5}

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

Compute the boundaries:

\frac{3093}{5}

= \frac{3093}{5}

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What is the integral from-1 to 2 of 2x(x^2+1)^4 ?
The integral from-1 to 2 of 2x(x^2+1)^4 is 3093/5