What is the integral from 0 to 2 of (x+1)^6 ?

The integral from 0 to 2 of (x+1)^6 is 2186/7

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integral from 0 to 2 of (x+1)^6

\int_{0}^{2} (x + 1)^{6} d x

\frac{2186}{7}

Decimal

312.28571 \dots

Solution steps

\int_{0}^{2} (x + 1)^{6} d x

Apply u-substitution

= \int_{1}^{3} u^{6} d u

Apply the Power Rule

= [\frac{u ^{7}}{7}]_{1}^{3}

Compute the boundaries:

\frac{2186}{7}

= \frac{2186}{7}

What is the integral from 0 to 2 of (x+1)^6 ?
The integral from 0 to 2 of (x+1)^6 is 2186/7