What is the integral of-5x^3+3/4 x^2 ?

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

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integral of-5x^3+3/4 x^2

\int - 5 x^{3} + \frac{3}{4} x^{2} d x

- \frac{5 x ^{4}}{4} + \frac{x ^{3}}{4} + C

Solution steps

\int - 5 x^{3} + \frac{3}{4} x^{2} 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 5 x^{3} d x + \int \frac{3}{4} x^{2} d x

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int \frac{3}{4} x^{2} d x = \frac{x ^{3}}{4}

= - \frac{5 x ^{4}}{4} + \frac{x ^{3}}{4}

Add a constant to the solution

= - \frac{5 x ^{4}}{4} + \frac{x ^{3}}{4} + C

\frac{d}{d x} ((e^{- x} - e^{5}) (e^{x} + e^{- 2}))

f (x) = \frac{5 x}{( 1 + x ^{2} )}

\frac{2 x}{( x + 1 ) ^{2}}

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

y^{^{'}} = \frac{( x ^{2} + y )}{x ^{3}}

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