What is the integral of-5sqrt(x^4) ?

The integral of-5sqrt(x^4) is -(5x^3)/3+C

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integral of-5sqrt(x^4)

\int - 5 x^{4} d x

- \frac{5 x ^{3}}{3} + C

Solution steps

\int - 5 x^{4} d x

Take the constant out:

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

= - 5 \cdot \int x^{4} d x

x^{4} = x^{2},

assuming

x \geq 0

= - 5 \cdot \int x^{2} d x

Apply the Power Rule

= - 5 \cdot \frac{x ^{3}}{3}

Multiply fractions:

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

= - \frac{5 x ^{3}}{3}

Add a constant to the solution

= - \frac{5 x ^{3}}{3} + C