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

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

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integral from 0 to 1 of x(θ+1)x^θ

\int_{0}^{1} x (θ + 1) x^{θ} d x

(1 + θ) \frac{1}{θ + 2}

Solution steps

\int_{0}^{1} x (θ + 1) x^{θ} d x

Take the constant out:

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

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

\int_{0}^{1} x x^{θ} d x = \frac{1}{θ + 2}

= (1 + θ) \frac{1}{θ + 2}

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