What is the integral of 8x^3sqrt(2x^4)+6 ?

The integral of 8x^3sqrt(2x^4)+6 is (4sqrt(2)x^6)/3+6x+C

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integral of 8x^3sqrt(2x^4)+6

\int 8 x^{3} 2 x^{4} + 6 d x

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

Solution steps

\int 8 x^{3} 2 x^{4} + 6 d x

8 x^{3} 2 x^{4} = 82 x^{5}

= \int 82 x^{5} + 6 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 82 x^{5} d x + \int 6 d x

\int 82 x^{5} d x = \frac{4 2 x ^{6}}{3}

\int 6 d x = 6 x

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

Add a constant to the solution

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

What is the integral of 8x^3sqrt(2x^4)+6 ?
The integral of 8x^3sqrt(2x^4)+6 is (4sqrt(2)x^6)/3+6x+C