Matematické Fórum

stuart clark · 23. 08. 2016 08:24

$\int e^{x^4}(x+x^3+2x^5)e^{x^2}dx$

Xellos · 24. 08. 2016 02:21 — Editoval Xellos (24. 08. 2016 02:45)

stuart clark · 24. 08. 2016 10:59

stuart clark · 26. 08. 2016 08:11

To ↑ Xellos: would you like to explain me how can i solve $\int \left(1+x-\frac{1}{x}\right)e^{x+\frac{1}{x}}$ using above Method

Xellos · 26. 08. 2016 18:59

↑ stuart clark:
I tried some clever methods and got nothing (the argument of that exponential is bad for substitution or per partes). Then I tried guesswork and found out that it's the derivative of $x e^{(x+1/x)}$ ...

stuart clark · 01. 09. 2016 07:58

Thanks ↑ Xellos:

Let $I = \int \left(1+x-\frac{1}{x}\right)e^{x+\frac{1}{x}}dx = \int x\cdot \left(1-\frac{1}{x^2}\right)e^{x+\frac{1}{x}}+e^{x+\frac{1}{x}}.1$

$= \int \left(x\cdot e^{x+\frac{1}{x}}\right)^{'}dx = x\cdot e^{x+\frac{1}{x}}+\mathcal{C}$

Matematické Fórum

#1 23. 08. 2016 08:24

Indefinite Integration

#2 24. 08. 2016 02:21 — Editoval Xellos (24. 08. 2016 02:45)

Re: Indefinite Integration

#3 24. 08. 2016 10:59

Re: Indefinite Integration

#4 26. 08. 2016 08:11

Re: Indefinite Integration

#5 26. 08. 2016 18:59

Re: Indefinite Integration

#6 01. 09. 2016 07:58

Re: Indefinite Integration

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