What is the integral of x^3(x^4+16)^3 ?

The integral of x^3(x^4+16)^3 is (x^{16})/(16)+4x^{12}+96x^8+1024x^4+C

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integral of x^3(x^4+16)^3

\int x^{3} (x^{4} + 16)^{3} d x

\frac{x ^{16}}{16} + 4 x^{12} + 96 x^{8} + 1024 x^{4} + C

Solution steps

\int x^{3} (x^{4} + 16)^{3} d x

Expand

x^{3} (x^{4} + 16)^{3} : x^{15} + 48 x^{11} + 768 x^{7} + 4096 x^{3}

= \int x^{15} + 48 x^{11} + 768 x^{7} + 4096 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 x^{15} d x + \int 48 x^{11} d x + \int 768 x^{7} d x + \int 4096 x^{3} d x

\int x^{15} d x = \frac{x ^{16}}{16}

\int 48 x^{11} d x = 4 x^{12}

\int 768 x^{7} d x = 96 x^{8}

\int 4096 x^{3} d x = 1024 x^{4}

= \frac{x ^{16}}{16} + 4 x^{12} + 96 x^{8} + 1024 x^{4}

Add a constant to the solution

= \frac{x ^{16}}{16} + 4 x^{12} + 96 x^{8} + 1024 x^{4} + C

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What is the integral of x^3(x^4+16)^3 ?
The integral of x^3(x^4+16)^3 is (x^{16})/(16)+4x^{12}+96x^8+1024x^4+C