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

The integral of (-xsqrt(x^4)) is -(x^4)/4+C

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integral of (-xsqrt(x^4))

\int (- x x^{4}) d x

- \frac{x ^{4}}{4} + C

Solution steps

\int - x x^{4} d x

Take the constant out:

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

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

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

assuming

x \geq 0

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

Simplify

x x^{2} : x^{3}

= - \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= - \frac{x ^{4}}{4}

Add a constant to the solution

= - \frac{x ^{4}}{4} + C

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What is the integral of (-xsqrt(x^4)) ?
The integral of (-xsqrt(x^4)) is -(x^4)/4+C