What is the integral of 32x^3-15x^2+10x ?

The integral of 32x^3-15x^2+10x is 8x^4-5x^3+5x^2+C

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integral of 32x^3-15x^2+10x

\int 32 x^{3} - 15 x^{2} + 10 x d x

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

Solution steps

\int 32 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 32 x^{3} d x - \int 15 x^{2} d x + \int 10 x d x

\int 32 x^{3} d x = 8 x^{4}

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

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

= 8 x^{4} - 5 x^{3} + 5 x^{2}

Add a constant to the solution

= 8 x^{4} - 5 x^{3} + 5 x^{2} + C

x + \frac{1}{y} = 2

\int \frac{2 x - 3}{( x - 1 ) ^{2}} d x

x^{2} - 6, x

\int (x^{3} + x)^{9} d x

y^{^{'}} + 5 y = x e^{- 5 x}

What is the integral of 32x^3-15x^2+10x ?
The integral of 32x^3-15x^2+10x is 8x^4-5x^3+5x^2+C