What is the integral of 32x^3-15x^2+8x ?

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

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integral of 32x^3-15x^2+8x

\int 32 x^{3} - 15 x^{2} + 8 x d x

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

Solution steps

\int 32 x^{3} - 15 x^{2} + 8 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 8 x d x

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

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

\int 8 x d x = 4 x^{2}

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

Add a constant to the solution

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

\int 2 x^{2} sin (3 x) d x

\int ln ((4 x)^{2}) d x

\int \frac{10 x}{5 x ^{2} + 1} d x

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

\frac{x ^{2} - 6 x + 1}{x ^{2} + 8}

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