How do you integrate $\int {(x^{2} \cdot 2 x \cdot 2)}^{2} d x$ $int (x^22x2)^2 dx$ ?

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Answer 1 · 2017-04-02T10:34:20

$16 x^{7} + c$ $16x^7+c$

First let's simplify the integrand.

${(x^{2} \cdot 2 x \cdot 2)}^{2} = {(4 x^{3})}^{2} = 16 x^{6}$ $(x^2*2x*2)^2 = (4x^3)^2 = 16x^6$

$I = \int 16 x^{6} d x$ $I= int 16x^6 dx$

$= 16 \cdot \int x^{6} d x$ $= 16 * int x^6 dx$

$= 16 \cdot \frac{x^{7}}{7} + c$ $= 16 * x^7/7 +c$ [Power rule}

$= 16 x^{7} + c$ $=16x^7+c$

How do you integrate ∫(x2⋅2x⋅2)2dxint (x^2*2x*2)^2 dx ?