What is the integral of x^3-3x^2+5x+2 ?

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

integral of x^3-3x^2+5x+2

integral

x^{3} - 3 x^{2} + 5 x + 2

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

Solution steps

\int x^{3} - 3 x^{2} + 5 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 x^{3} d x - \int 3 x^{2} d x + \int 5 x d x + \int 2 d x

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

in t e g r a l (e^{- t}) \cdot (\frac{1}{t})

in t e g r a l x^{2} + a^{2}

s im pl i f y (\frac{1}{x - 1})^{\frac{1}{2}}

in t e g r a l \frac{2 x ^{2}}{( x ^{2} + 1 )}

in t e g r a l 2 - x^{2}

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