What is the integral from-2 to 4 of (x^2+4)^34x ?

The integral from-2 to 4 of (x^2+4)^34x is 77952

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integral from-2 to 4 of (x^2+4)^34x

\int_{- 2}^{4} (x^{2} + 4)^{3} 4 x d x

77952

Solution steps

\int_{- 2}^{4} (x^{2} + 4)^{3} \cdot 4 x d x

Take the constant out:

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

= 4 \cdot \int_{- 2}^{4} (x^{2} + 4)^{3} x d x

Apply u-substitution

: \int_{8}^{20} \frac{u ^{3}}{2} d u

= 4 \cdot \int_{8}^{20} \frac{u ^{3}}{2} d u

Take the constant out:

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

= 4 \cdot \frac{1}{2} \cdot \int_{8}^{20} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{8}^{20}

= 4 \cdot \frac{1}{2} [\frac{u ^{4}}{4}]_{8}^{20}

Simplify

4 \cdot \frac{1}{2} [\frac{u ^{4}}{4}]_{8}^{20} : 2 [\frac{u ^{4}}{4}]_{8}^{20}

= 2 [\frac{u ^{4}}{4}]_{8}^{20}

Compute the boundaries:

38976

= 2 \cdot 38976

Simplify

= 77952

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What is the integral from-2 to 4 of (x^2+4)^34x ?
The integral from-2 to 4 of (x^2+4)^34x is 77952