What is the integral from 4 to 5 of (5x+2)^7 ?

The integral from 4 to 5 of (5x+2)^7 is (27^8-54875873536)/(40)

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integral from 4 to 5 of (5x+2)^7

\int_{4}^{5} (5 x + 2)^{7} d x

\frac{2 7 ^{8} - 54875873536}{40}

Decimal

5688841573.625

Solution steps

\int_{4}^{5} (5 x + 2)^{7} d x

Apply u-substitution

= \int_{22}^{27} \frac{u ^{7}}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{22}^{27} u^{7} d u

Apply the Power Rule

= \frac{1}{5} [\frac{u ^{8}}{8}]_{22}^{27}

Compute the boundaries:

\frac{2 7 ^{8}}{8} - 6859484192

= \frac{1}{5} (\frac{2 7 ^{8}}{8} - 6859484192)

Simplify

= \frac{2 7 ^{8} - 54875873536}{40}

What is the integral from 4 to 5 of (5x+2)^7 ?
The integral from 4 to 5 of (5x+2)^7 is (27^8-54875873536)/(40)