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

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

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integral of x^2*(x-5)+sqrt(7-x)

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

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

Solution steps

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

\int x^{2} (x - 5) d x = \frac{x ^{4}}{4} - \frac{5 x ^{3}}{3}

\int 7 - x d x = - \frac{2}{3} (7 - x)^{\frac{3}{2}}

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

Add a constant to the solution

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

\int - 4 e^{x} d x

\int_{0}^{2} 2 π x (3 x (x - 2)^{2}) d x

n = 1 \sum \infty \frac{2 n}{3 n - 1}

\frac{d}{d x} (\frac{3 a}{4 x ^{5}})

\frac{x ^{2} + 4 x}{( 2 + x ) ^{2}}

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