What is the integral of x^3-2x^2-x+1 ?

The integral of x^3-2x^2-x+1 is (x^4)/4-(2x^3)/3-(x^2)/2+x+C

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integral of x^3-2x^2-x+1

integral

x^{3} - 2 x^{2} - x + 1

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

Solution steps

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

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

\frac{4}{3 x - 2}

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

\frac{( y + 1 )}{y ^{3}}

\frac{tan ( x )}{2}

\frac{ln ( t )}{( 1 + t ^{2} )}

What is the integral of x^3-2x^2-x+1 ?
The integral of x^3-2x^2-x+1 is (x^4)/4-(2x^3)/3-(x^2)/2+x+C