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Popular >

integral of-x^3-8x+5

Solution

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

Solution

- \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

Popular Examples

limit as x approaches 0 of 1/(x+x^5)

x \to 0 lim (\frac{1}{x + x ^{5}})

area 2x^2-x^3,y=0 area

2 x^{2} - x^{3}, y = 0

integral of-3/2 x^2

\int - \frac{3}{2} x^{2} d x

integral of (tan(x/(18)))^5

\int (tan (\frac{x}{18}))^{5} d x

derivative of (4x/((1-x^2)^2))

\frac{d}{d x} (\frac{4 x}{( 1 - x ^{2} ) ^{2}})

Frequently Asked Questions (FAQ)

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