What is the integral of (x^3-2x^2+7x+5) ?

The integral of (x^3-2x^2+7x+5) is (x^4)/4-(2x^3)/3+(7x^2)/2+5x+C

Popular >

integral of (x^3-2x^2+7x+5)

\int (x^{3} - 2 x^{2} + 7 x + 5) d x

\frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} + \frac{7 x ^{2}}{2} + 5 x + C

Solution steps

\int x^{3} - 2 x^{2} + 7 x + 5 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 7 x d x + \int 5 d x

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

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

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 5 d x = 5 x

= \frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} + \frac{7 x ^{2}}{2} + 5 x

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} + \frac{7 x ^{2}}{2} + 5 x + C

\int 10 tan^{9} (x) sec^{2} (x) d x

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

\int \frac{x ^{2} - 4 x - 2}{x ^{3} - 2 x ^{2} + 4 x - 8} d x

\int (3 x + 4) e^{x} d x

\int cot^{4} (y) d y

What is the integral of (x^3-2x^2+7x+5) ?
The integral of (x^3-2x^2+7x+5) is (x^4)/4-(2x^3)/3+(7x^2)/2+5x+C