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

The integral from 0 to 1 of (θ+2)x^{θ+1}x is (2+θ) 1/(θ+3)

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integral from 0 to 1 of (θ+2)x^{θ+1}x

\int_{0}^{1} (θ + 2) x^{θ + 1} x d x

(2 + θ) \frac{1}{θ + 3}

Solution steps

\int_{0}^{1} (θ + 2) x^{θ + 1} x d x

Take the constant out:

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

= (2 + θ) \cdot \int_{0}^{1} x x^{1 + θ} d x

\int_{0}^{1} x x^{1 + θ} d x = \frac{1}{θ + 3}

= (2 + θ) \frac{1}{θ + 3}

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