What is the integral of 24x^3-15x^2+10x ?

The integral of 24x^3-15x^2+10x is 6x^4-5x^3+5x^2+C

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integral of 24x^3-15x^2+10x

\int 24 x^{3} - 15 x^{2} + 10 x d x

6 x^{4} - 5 x^{3} + 5 x^{2} + C

Solution steps

\int 24 x^{3} - 15 x^{2} + 10 x 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 24 x^{3} d x - \int 15 x^{2} d x + \int 10 x d x

\int 24 x^{3} d x = 6 x^{4}

\int 15 x^{2} d x = 5 x^{3}

\int 10 x d x = 5 x^{2}

= 6 x^{4} - 5 x^{3} + 5 x^{2}

Add a constant to the solution

= 6 x^{4} - 5 x^{3} + 5 x^{2} + C

\int \frac{1}{x \cdot 1 + x ^{2}} d x

\int (x^{2} + 15) (x^{4} - 9) d x

\int t \cdot e^{2 t} d t

\int (x + 8)^{4} d x

\int e^{- \frac{t ^{2}}{2}} d t

What is the integral of 24x^3-15x^2+10x ?
The integral of 24x^3-15x^2+10x is 6x^4-5x^3+5x^2+C