What is the integral of 2x^3-6x^2+4x ?

The integral of 2x^3-6x^2+4x is (x^4)/2-2x^3+2x^2+C

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integral of 2x^3-6x^2+4x

\int 2 x^{3} - 6 x^{2} + 4 x d x

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

Solution steps

\int 2 x^{3} - 6 x^{2} + 4 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 6 x^{2} d x + \int 4 x d x

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

\int 6 x^{2} d x = 2 x^{3}

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

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

Add a constant to the solution

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

\int \frac{4 ^{x}}{2 ^{x} - 1} d x

\int e^{1 + x^{2}} d x

\int \frac{x}{( x + 1 )} d x

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

\int \frac{1 - x}{9 - 4 x} d x

What is the integral of 2x^3-6x^2+4x ?
The integral of 2x^3-6x^2+4x is (x^4)/2-2x^3+2x^2+C