e-x-1-x-2-dx-

Question Number 44654 by manish00@gmail.com last updated on 02/Oct/18

\int \frac{e^{x}}{1 + x^{2}} dx = ?

Commented by maxmathsup by imad last updated on 02/Oct/18

c h a n g e m e n t x = t a n θ g i v e I = \int \frac{e^{t a n θ}}{1 + {t a n}^{2} θ} (1 + {t a n}^{2} θ) d θ

= \int e^{t a n θ} d θ = \int (\sum_{n = 0}^{\infty} \frac{{(t a n θ)}^{n}}{n!}) d θ

= \sum_{n = 0}^{\infty} \frac{1}{n!} \int {t a n}^{n} d θ a n d A_{n} = \int {t a n}^{n} θ d θ c a n b e c a l c u l a t e d b y r e c u r r e n c e \dots

Commented by maxmathsup by imad last updated on 02/Oct/18

w e h a v e e^{x} = \sum_{n = 0}^{\infty} \frac{x^{n}}{n!} \Rightarrow \int \frac{e^{x}}{1 + x^{2}} d x = \int \frac{1}{1 + x^{2}} (\sum_{n = 0}^{\infty} \frac{x^{n}}{n!}) d x

= \sum_{n = 0}^{\infty} \frac{1}{n!} \int \frac{x^{n}}{1 + x^{2}} d x = \sum_{n = 0}^{\infty} \frac{A_{n}}{n!} w i t h A_{n} = \int \frac{x^{n}}{1 + x^{2}} d x \dots .

Commented by maxmathsup by imad last updated on 02/Oct/18

i t h i n k t h i s i n t e g r a l c a n t b e c a l c u l a t e d b y e l e m e n t a r y f u n c t i o n s \dots

Commented by arvinddayama01@gmail.com last updated on 03/Oct/18

T h a n k u s i r

Answered by tanmay.chaudhury50@gmail.com last updated on 02/Oct/18

i s i t f e a s i b l e \dots