What is the integral of x^3(4x^2+5) ?

The integral of x^3(4x^2+5) is (2x^6)/3+(5x^4)/4+C

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integral of x^3(4x^2+5)

\int x^{3} (4 x^{2} + 5) d x

\frac{2 x ^{6}}{3} + \frac{5 x ^{4}}{4} + C

Solution steps

\int x^{3} (4 x^{2} + 5) d x

Expand

x^{3} (4 x^{2} + 5) : 4 x^{5} + 5 x^{3}

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

\int 4 x^{5} d x = \frac{2 x ^{6}}{3}

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

= \frac{2 x ^{6}}{3} + \frac{5 x ^{4}}{4}

Add a constant to the solution

= \frac{2 x ^{6}}{3} + \frac{5 x ^{4}}{4} + C

\int \frac{1}{x ^{\frac{9}{2}}} d x

\frac{6 ( s + 34 )}{s ( s ^{2} + 10 s + 34 )}

f (x) = x^{4} + 5 e^{x}, (0, 5)

f (x) = a x

\int_{- \infty}^{0} x \cdot e^{x} d x

What is the integral of x^3(4x^2+5) ?
The integral of x^3(4x^2+5) is (2x^6)/3+(5x^4)/4+C