What is the integral of (4x^2-3x)^4(8x-3) ?

The integral of (4x^2-3x)^4(8x-3) is (1024x^{10})/5-768x^9+1152x^8-864x^7+324x^6-(243x^5)/5+C

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integral of (4x^2-3x)^4(8x-3)

\int (4 x^{2} - 3 x)^{4} (8 x - 3) d x

\frac{1024 x ^{10}}{5} - 768 x^{9} + 1152 x^{8} - 864 x^{7} + 324 x^{6} - \frac{243 x ^{5}}{5} + C

Solution steps

\int (4 x^{2} - 3 x)^{4} (8 x - 3) d x

Expand

(4 x^{2} - 3 x)^{4} (8 x - 3) : 2048 x^{9} - 6912 x^{8} + 9216 x^{7} - 6048 x^{6} + 1944 x^{5} - 243 x^{4}

= \int 2048 x^{9} - 6912 x^{8} + 9216 x^{7} - 6048 x^{6} + 1944 x^{5} - 243 x^{4} 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 2048 x^{9} d x - \int 6912 x^{8} d x + \int 9216 x^{7} d x - \int 6048 x^{6} d x + \int 1944 x^{5} d x - \int 243 x^{4} d x

\int 2048 x^{9} d x = \frac{1024 x ^{10}}{5}

\int 6912 x^{8} d x = 768 x^{9}

\int 9216 x^{7} d x = 1152 x^{8}

\int 6048 x^{6} d x = 864 x^{7}

\int 1944 x^{5} d x = 324 x^{6}

\int 243 x^{4} d x = \frac{243 x ^{5}}{5}

= \frac{1024 x ^{10}}{5} - 768 x^{9} + 1152 x^{8} - 864 x^{7} + 324 x^{6} - \frac{243 x ^{5}}{5}

Add a constant to the solution

= \frac{1024 x ^{10}}{5} - 768 x^{9} + 1152 x^{8} - 864 x^{7} + 324 x^{6} - \frac{243 x ^{5}}{5} + C

\frac{d}{d t} (t + sin (t))

\int \frac{1}{5} e^{5 x} d x

n = 1 \sum \infty 4 (\frac{3}{2})^{n - 1}

\frac{d y}{d x} = \frac{y ( x - y )}{x ^{2}}

\frac{d}{d x} (sin (x) \cdot cos (x) \cdot \frac{1}{x})

What is the integral of (4x^2-3x)^4(8x-3) ?
The integral of (4x^2-3x)^4(8x-3) is (1024x^{10})/5-768x^9+1152x^8-864x^7+324x^6-(243x^5)/5+C