What is the integral of xy^2z^2 ?

The integral of xy^2z^2 is (y^2z^2x^2)/2+C

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integral of xy^2z^2

\int x y^{2} z^{2} d x

\frac{y ^{2} z ^{2} x ^{2}}{2} + C

Solution steps

\int x y^{2} z^{2} d x

Take the constant out:

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

= y^{2} z^{2} \cdot \int x d x

Apply the Power Rule

= y^{2} z^{2} \frac{x ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{y ^{2} z ^{2} x ^{2}}{2}

Add a constant to the solution

= \frac{y ^{2} z ^{2} x ^{2}}{2} + C