What is the integral from 0 to 1 of (3x-1)^{50} ?

The integral from 0 to 1 of (3x-1)^{50} is (2^{51}+1)/(153)

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integral from 0 to 1 of (3x-1)^{50}

\int_{0}^{1} (3 x - 1)^{50} d x

\frac{2 ^{51} + 1}{153}

Decimal

1.47176 E 13

Solution steps

\int_{0}^{1} (3 x - 1)^{50} d x

Apply u-substitution

: \int_{- 1}^{2} \frac{u ^{50}}{3} d u

= \int_{- 1}^{2} \frac{u ^{50}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{- 1}^{2} u^{50} d u

Apply the Power Rule

: [\frac{u ^{51}}{51}]_{- 1}^{2}

= \frac{1}{3} [\frac{u ^{51}}{51}]_{- 1}^{2}

Compute the boundaries:

\frac{2 ^{51}}{51} + \frac{1}{51}

= \frac{1}{3} (\frac{2 ^{51}}{51} + \frac{1}{51})

Simplify

= \frac{2 ^{51} + 1}{153}

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What is the integral from 0 to 1 of (3x-1)^{50} ?
The integral from 0 to 1 of (3x-1)^{50} is (2^{51}+1)/(153)