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

The integral of 2x^3+3x^2-10x is (x^4)/2+x^3-5x^2+C

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

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\int \frac{a}{cos ^{2} ( b x )} d x

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

What is the integral of 2x^3+3x^2-10x ?
The integral of 2x^3+3x^2-10x is (x^4)/2+x^3-5x^2+C