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

The integral of x^2(3-e^{x^3}) is x^3-1/3 e^{x^3}+C

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integral of x^2(3-e^{x^3})

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

x^{3} - \frac{1}{3} e^{x^{3}} + C

Solution steps

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

Apply Integration By Parts

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

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

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

= \frac{1}{3} x^{3} (3 - e^{x^{3}}) - (- \frac{1}{3} (e^{x^{3}} x^{3} - e^{x^{3}}))

Simplify

\frac{1}{3} x^{3} (3 - e^{x^{3}}) - (- \frac{1}{3} (e^{x^{3}} x^{3} - e^{x^{3}})) : x^{3} - \frac{1}{3} e^{x^{3}}

= x^{3} - \frac{1}{3} e^{x^{3}}

Add a constant to the solution

= x^{3} - \frac{1}{3} e^{x^{3}} + C

x \to \infty lim (e^{- \frac{2}{x}})

\frac{2}{s}

\int_{1}^{2} 0 d x

\int_{- \infty}^{- 1} x^{- \frac{11}{5}} d x

\int e^{3 x} d x

What is the integral of x^2(3-e^{x^3}) ?
The integral of x^2(3-e^{x^3}) is x^3-1/3 e^{x^3}+C