What is the integral of (7x^5+2)^3 ?

The integral of (7x^5+2)^3 is (343x^{16})/(16)+(294x^{11})/(11)+14x^6+8x+C

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integral of (7x^5+2)^3

\int (7 x^{5} + 2)^{3} d x

\frac{343 x ^{16}}{16} + \frac{294 x ^{11}}{11} + 14 x^{6} + 8 x + C

Solution steps

\int (7 x^{5} + 2)^{3} d x

Expand

(7 x^{5} + 2)^{3} : 343 x^{15} + 294 x^{10} + 84 x^{5} + 8

= \int 343 x^{15} + 294 x^{10} + 84 x^{5} + 8 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 343 x^{15} d x + \int 294 x^{10} d x + \int 84 x^{5} d x + \int 8 d x

\int 343 x^{15} d x = \frac{343 x ^{16}}{16}

\int 294 x^{10} d x = \frac{294 x ^{11}}{11}

\int 84 x^{5} d x = 14 x^{6}

\int 8 d x = 8 x

= \frac{343 x ^{16}}{16} + \frac{294 x ^{11}}{11} + 14 x^{6} + 8 x

Add a constant to the solution

= \frac{343 x ^{16}}{16} + \frac{294 x ^{11}}{11} + 14 x^{6} + 8 x + C

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What is the integral of (7x^5+2)^3 ?
The integral of (7x^5+2)^3 is (343x^{16})/(16)+(294x^{11})/(11)+14x^6+8x+C