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

The integral from 2 to 4 of (2x+4)^4 is 108032/5

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

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

\frac{108032}{5}

Decimal

21606.4

Solution steps

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

Apply u-substitution

: \int_{8}^{12} \frac{u ^{4}}{2} d u

= \int_{8}^{12} \frac{u ^{4}}{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_{8}^{12} u^{4} d u

Apply the Power Rule

: [\frac{u ^{5}}{5}]_{8}^{12}

= \frac{1}{2} [\frac{u ^{5}}{5}]_{8}^{12}

Compute the boundaries:

\frac{216064}{5}

= \frac{1}{2} \cdot \frac{216064}{5}

Simplify

= \frac{108032}{5}

\int_{- 3}^{- 1} x - 4 d x

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

\int_{1}^{2} \frac{( x ^{2} - 1 )}{x ^{3}} d x

\int_{1}^{2} (x - 1)^{- 3} d x

\int_{0}^{6} \frac{185}{( t + 1 ) ^{2}} d t

What is the integral from 2 to 4 of (2x+4)^4 ?
The integral from 2 to 4 of (2x+4)^4 is 108032/5