What is the integral of x^2(8x^3+7)^2 ?

The integral of x^2(8x^3+7)^2 is (64x^9)/9+56/3 x^6+49/3 x^3+C

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integral of x^2(8x^3+7)^2

\int x^{2} (8 x^{3} + 7)^{2} d x

\frac{64 x ^{9}}{9} + \frac{56}{3} x^{6} + \frac{49}{3} x^{3} + C

Solution steps

\int x^{2} (8 x^{3} + 7)^{2} d x

Apply Integration By Parts

: \frac{1}{3} x^{3} (8 x^{3} + 7)^{2} - \int 16 x^{5} (8 x^{3} + 7) d x

= \frac{1}{3} x^{3} (8 x^{3} + 7)^{2} - \int 16 x^{5} (8 x^{3} + 7) d x

\int 16 x^{5} (8 x^{3} + 7) d x = 16 (\frac{1}{6} x^{6} (8 x^{3} + 7) - \frac{4 x ^{9}}{9})

= \frac{1}{3} x^{3} (8 x^{3} + 7)^{2} - 16 (\frac{1}{6} x^{6} (8 x^{3} + 7) - \frac{4 x ^{9}}{9})

Simplify

\frac{1}{3} x^{3} (8 x^{3} + 7)^{2} - 16 (\frac{1}{6} x^{6} (8 x^{3} + 7) - \frac{4 x ^{9}}{9}) : \frac{64 x ^{9}}{9} + \frac{56}{3} x^{6} + \frac{49}{3} x^{3}

= \frac{64 x ^{9}}{9} + \frac{56}{3} x^{6} + \frac{49}{3} x^{3}

Add a constant to the solution

= \frac{64 x ^{9}}{9} + \frac{56}{3} x^{6} + \frac{49}{3} x^{3} + C

\frac{d}{d x} (arctan (7^{x}))

\int \frac{( e ^{a r c t a n (x)} )}{1 + x ^{2}} d x

x \to 0 lim (\frac{5 sin ( 2 x )}{x})

t e^{5 t}

w \to - 2 lim (\frac{w + 2}{w ^{2} - 6 w - 16})

What is the integral of x^2(8x^3+7)^2 ?
The integral of x^2(8x^3+7)^2 is (64x^9)/9+56/3 x^6+49/3 x^3+C