What is the integral of (-x^3-8x+5) ?

The integral of (-x^3-8x+5) is -(x^4)/4-4x^2+5x+C

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integral of (-x^3-8x+5)

\int (- x^{3} - 8 x + 5) d x

- \frac{x ^{4}}{4} - 4 x^{2} + 5 x + C

Solution steps

\int - x^{3} - 8 x + 5 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int x^{3} d x - \int 8 x d x + \int 5 d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int 8 x d x = 4 x^{2}

\int 5 d x = 5 x

= - \frac{x ^{4}}{4} - 4 x^{2} + 5 x

Add a constant to the solution

= - \frac{x ^{4}}{4} - 4 x^{2} + 5 x + C

\int_{0}^{2 π} 5 x^{2} sin (\frac{1}{4} x) d x

\frac{d}{d x} (\frac{1}{3} x x^{2} + 5)

\int \frac{1}{- 4 t ^{2} + 12 t + 7} d t

\int_{0}^{π} sin (x^{2}) d x

\int cos (t) + sin^{3} (t) d t

What is the integral of (-x^3-8x+5) ?
The integral of (-x^3-8x+5) is -(x^4)/4-4x^2+5x+C