What is the integral of x^3-5x^2-7x+35 ?

The integral of x^3-5x^2-7x+35 is (x^4)/4-(5x^3)/3-(7x^2)/2+35x+C

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integral of x^3-5x^2-7x+35

\int x^{3} - 5 x^{2} - 7 x + 35 d x

\frac{x ^{4}}{4} - \frac{5 x ^{3}}{3} - \frac{7 x ^{2}}{2} + 35 x + C

Solution steps

\int x^{3} - 5 x^{2} - 7 x + 35 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 5 x^{2} d x - \int 7 x d x + \int 35 d x

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

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

\int 35 d x = 35 x

= \frac{x ^{4}}{4} - \frac{5 x ^{3}}{3} - \frac{7 x ^{2}}{2} + 35 x

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{5 x ^{3}}{3} - \frac{7 x ^{2}}{2} + 35 x + C

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What is the integral of x^3-5x^2-7x+35 ?
The integral of x^3-5x^2-7x+35 is (x^4)/4-(5x^3)/3-(7x^2)/2+35x+C