What is the integral of (3x^2-2)^2 ?

The integral of (3x^2-2)^2 is 9x^5-(36x^5)/5-4x^3+4x+C

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integral of (3x^2-2)^2

\int (3 x^{2} - 2)^{2} d x

9 x^{5} - \frac{36 x ^{5}}{5} - 4 x^{3} + 4 x + C

Solution steps

\int (3 x^{2} - 2)^{2} d x

Apply Integration By Parts

: x (3 x^{2} - 2)^{2} - \int 12 x^{2} (3 x^{2} - 2) d x

= x (3 x^{2} - 2)^{2} - \int 12 x^{2} (3 x^{2} - 2) d x

\int 12 x^{2} (3 x^{2} - 2) d x = 12 (\frac{3 x ^{5}}{5} - \frac{2 x ^{3}}{3})

= x (3 x^{2} - 2)^{2} - 12 (\frac{3 x ^{5}}{5} - \frac{2 x ^{3}}{3})

Simplify

x (3 x^{2} - 2)^{2} - 12 (\frac{3 x ^{5}}{5} - \frac{2 x ^{3}}{3}) : 9 x^{5} - \frac{36 x ^{5}}{5} - 4 x^{3} + 4 x

= 9 x^{5} - \frac{36 x ^{5}}{5} - 4 x^{3} + 4 x

Add a constant to the solution

= 9 x^{5} - \frac{36 x ^{5}}{5} - 4 x^{3} + 4 x + C

f (x) = x^{2} + 5

y^{^{'}} = - \frac{9 x}{16 y}

y^{^{''}} + y = 3 e^{- 8 x}, y (0) = 0, y^{^{'}} (0) = 0

x \to 4 lim (16 - x^{2})

x \to - 2 lim (5)

What is the integral of (3x^2-2)^2 ?
The integral of (3x^2-2)^2 is 9x^5-(36x^5)/5-4x^3+4x+C