What is the integral of x(x^2-3)^{2022} ?

The integral of x(x^2-3)^{2022} is 1/4046 (x^2-3)^{2023}+C

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integral of x(x^2-3)^{2022}

\int x (x^{2} - 3)^{2022} d x

\frac{1}{4046} (x^{2} - 3)^{2023} + C

Solution steps

\int x (x^{2} - 3)^{2022} d x

Apply u-substitution

: \int \frac{u ^{2022}}{2} d u

= \int \frac{u ^{2022}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{2022} d u

Apply the Power Rule

: \frac{u ^{2023}}{2023}

= \frac{1}{2} \cdot \frac{u ^{2023}}{2023}

Substitute back

u = x^{2} - 3

= \frac{1}{2} \cdot \frac{( x ^{2} - 3 ) ^{2023}}{2023}

Simplify

\frac{1}{2} \cdot \frac{( x ^{2} - 3 ) ^{2023}}{2023} : \frac{1}{4046} (x^{2} - 3)^{2023}

= \frac{1}{4046} (x^{2} - 3)^{2023}

Add a constant to the solution

= \frac{1}{4046} (x^{2} - 3)^{2023} + C

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What is the integral of x(x^2-3)^{2022} ?
The integral of x(x^2-3)^{2022} is 1/4046 (x^2-3)^{2023}+C