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

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

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

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\int (z + 1) e^{8 z} d z

\frac{1}{( x + y ) ^{2}}

\int (2 - e) d x

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