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

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

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integral of (2x^3+3x^2+x-2)

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

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

Solution steps

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

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

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\int \frac{sin ^{3} ( 4 x )}{cos ( 4 x )} d x

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