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

The integral of x^3(2x+5-3sqrt(x)) is (2x^5)/5+(5x^4)/4-2/3 x^{9/2}+C

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

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

\frac{2 x ^{5}}{5} + \frac{5 x ^{4}}{4} - \frac{2}{3} x^{\frac{9}{2}} + C

Solution steps

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

Expand

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

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

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 3 x^{\frac{7}{2}} d x = \frac{2}{3} x^{\frac{9}{2}}

= \frac{2 x ^{5}}{5} + \frac{5 x ^{4}}{4} - \frac{2}{3} x^{\frac{9}{2}}

Add a constant to the solution

= \frac{2 x ^{5}}{5} + \frac{5 x ^{4}}{4} - \frac{2}{3} x^{\frac{9}{2}} + C

n = 1 \sum \infty e^{2 n}

\frac{d}{d x} (x cos (y) - y cos (x))

e^{t^{2}}

\frac{( s - 1 )}{s ( s ^{2} + s + 1 )}

\int \frac{x}{( 1 + x ^{2} ) 1 - x ^{4}} d x

What is the integral of x^3(2x+5-3sqrt(x)) ?
The integral of x^3(2x+5-3sqrt(x)) is (2x^5)/5+(5x^4)/4-2/3 x^{9/2}+C