What is the integral of (-3x^4+6x^3-5x^2) ?

The integral of (-3x^4+6x^3-5x^2) is -(3x^5)/5+(3x^4)/2-(5x^3)/3+C

Popular >

integral of (-3x^4+6x^3-5x^2)

\int (- 3 x^{4} + 6 x^{3} - 5 x^{2}) d x

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

Solution steps

\int - 3 x^{4} + 6 x^{3} - 5 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 3 x^{4} d x + \int 6 x^{3} d x - \int 5 x^{2} d x

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

\int 6 x^{3} d x = \frac{3 x ^{4}}{2}

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

Add a constant to the solution

= - \frac{3 x ^{5}}{5} + \frac{3 x ^{4}}{2} - \frac{5 x ^{3}}{3} + C

\frac{d}{d x} (\frac{1}{8} x - ln (2 x))

f (x) = 5 x ln (x)

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

\int \frac{6}{3 x} d x

y = t^{3} - 2 t + 4

What is the integral of (-3x^4+6x^3-5x^2) ?
The integral of (-3x^4+6x^3-5x^2) is -(3x^5)/5+(3x^4)/2-(5x^3)/3+C