What is the integral of 2x^3-2/3 x^2+9x ?

The integral of 2x^3-2/3 x^2+9x is (x^4)/2-(2x^3)/9+(9x^2)/2+C

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integral of 2x^3-2/3 x^2+9x

\int 2 x^{3} - \frac{2}{3} x^{2} + 9 x d x

\frac{x ^{4}}{2} - \frac{2 x ^{3}}{9} + \frac{9 x ^{2}}{2} + C

Solution steps

\int 2 x^{3} - \frac{2}{3} x^{2} + 9 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 \frac{2}{3} x^{2} d x + \int 9 x d x

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

\int \frac{2}{3} x^{2} d x = \frac{2 x ^{3}}{9}

\int 9 x d x = \frac{9 x ^{2}}{2}

= \frac{x ^{4}}{2} - \frac{2 x ^{3}}{9} + \frac{9 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{4}}{2} - \frac{2 x ^{3}}{9} + \frac{9 x ^{2}}{2} + C

\int \frac{12}{( 1 + x + y ) ^{5}} d y

x^{2} y^{^{'}} + x (x + 2) y = e x

x \to 0 lim (3^{s i n (\frac{1}{x})})

\frac{d y}{d x} + \frac{1}{x} y = 2

\frac{d}{d x} (3^{l n (x)})

What is the integral of 2x^3-2/3 x^2+9x ?
The integral of 2x^3-2/3 x^2+9x is (x^4)/2-(2x^3)/9+(9x^2)/2+C