Question

integrala din 3 x^3 ori e^x^3

Answer 1

[tex]\int \:3\:x^3\:\cdot \:e^x^3 \\ =\ \textgreater \ 3\cdot \int \:x^3e^{x\cdot \:3}dx \\ =\ \textgreater \ 3\cdot \int \:\frac{e^uu^3}{81}du \\ =\ \textgreater \ 3\cdot \frac{1}{81}\cdot \int \:e^uu^3du \\ =\ \textgreater \ 3\cdot \frac{1}{81}\left(u^3e^u-\int \:3u^2e^udu\right) [/tex]

[tex]\\ =\ \textgreater \ 3\cdot \frac{1}{81}\left(u^3e^u-3\left(u^2e^u-2\left(e^uu-e^u\right)\right)\right) \\ =\ \textgreater \ 3\cdot \frac{1}{81}\left(\left(x\cdot \:3\right)^3e^{x\cdot \:3}-3\left(\left(x\cdot \:3\right)^2e^{x\cdot \:3}-2\left(e^{x\cdot \:3}x\cdot \:3-e^{x\cdot \:3}\right)\right)\right) \\ =\ \textgreater \ \boxed{\frac{1}{9}e^{3x}\left(9x^3-9x^2+6x-2\right)}[/tex]