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

The integral of x(4x+5)^3 is (64x^5)/5+60x^4+100x^3+(125x^2)/2+C

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integral of x(4x+5)^3

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

\frac{64 x ^{5}}{5} + 60 x^{4} + 100 x^{3} + \frac{125 x ^{2}}{2} + C

Solution steps

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

Expand

x (4 x + 5)^{3} : 64 x^{4} + 240 x^{3} + 300 x^{2} + 125 x

= \int 64 x^{4} + 240 x^{3} + 300 x^{2} + 125 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 64 x^{4} d x + \int 240 x^{3} d x + \int 300 x^{2} d x + \int 125 x d x

\int 64 x^{4} d x = \frac{64 x ^{5}}{5}

\int 240 x^{3} d x = 60 x^{4}

\int 300 x^{2} d x = 100 x^{3}

\int 125 x d x = \frac{125 x ^{2}}{2}

= \frac{64 x ^{5}}{5} + 60 x^{4} + 100 x^{3} + \frac{125 x ^{2}}{2}

Add a constant to the solution

= \frac{64 x ^{5}}{5} + 60 x^{4} + 100 x^{3} + \frac{125 x ^{2}}{2} + C

\frac{d y}{d x}, x y = 28

(- 1.2) (- 2.3)

\int sin^{4} (y) cos (y) d y

\frac{d}{d x} (\frac{0.001 x}{0.001 x + 1})

What is the integral of x(4x+5)^3 ?
The integral of x(4x+5)^3 is (64x^5)/5+60x^4+100x^3+(125x^2)/2+C