What is the integral of x(-4-7x^4) ?

The integral of x(-4-7x^4) is 1/2 x^2(-4-7x^4)+(7x^6)/3+C

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integral of x(-4-7x^4)

\int x (- 4 - 7 x^{4}) d x

\frac{1}{2} x^{2} (- 4 - 7 x^{4}) + \frac{7 x ^{6}}{3} + C

Solution steps

\int x (- 4 - 7 x^{4}) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} (- 4 - 7 x^{4}) - \int - 14 x^{5} d x

= \frac{1}{2} x^{2} (- 4 - 7 x^{4}) - \int - 14 x^{5} d x

\int - 14 x^{5} d x = - \frac{7 x ^{6}}{3}

= \frac{1}{2} x^{2} (- 4 - 7 x^{4}) - (- \frac{7 x ^{6}}{3})

Simplify

= \frac{1}{2} x^{2} (- 4 - 7 x^{4}) + \frac{7 x ^{6}}{3}

Add a constant to the solution

= \frac{1}{2} x^{2} (- 4 - 7 x^{4}) + \frac{7 x ^{6}}{3} + C

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What is the integral of x(-4-7x^4) ?
The integral of x(-4-7x^4) is 1/2 x^2(-4-7x^4)+(7x^6)/3+C