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

The integral of x^2(2x^3-5) is 1/3 x^3(2x^3-5)-(x^6)/3+C

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integral of x^2(2x^3-5)

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

\frac{1}{3} x^{3} (2 x^{3} - 5) - \frac{x ^{6}}{3} + C

Solution steps

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

Apply Integration By Parts

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

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

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

= \frac{1}{3} x^{3} (2 x^{3} - 5) - \frac{x ^{6}}{3}

Add a constant to the solution

= \frac{1}{3} x^{3} (2 x^{3} - 5) - \frac{x ^{6}}{3} + C

f (x) = sin^{2} (x^{2})

x \to π lim (cot (x))

\frac{d}{d x} (\frac{1}{8 x ^{\frac{7}{8}}})

\frac{d}{d x} (7 cos^{3} (x))

2 x^{2} \frac{d y}{d x} = π y sin (\frac{π}{2 x})

What is the integral of x^2(2x^3-5) ?
The integral of x^2(2x^3-5) is 1/3 x^3(2x^3-5)-(x^6)/3+C