intleft(1+x-x^{-1}right) e^{x+x^{-1}} d x is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $I = \int (1 + x - x^{-1}) e^{x + x^{-1}} dx$. We can rewrite the integral as: $I = \int e^{x + x^{-1}} dx + \int (x - x^{-1}) e^{x + x^{-1}}

Vedclass · Accepted Answer

$x e^{x+x^{-1}}+C$

Vedclass · Answer

(D) Let $I = \int (1 + x - x^{-1}) e^{x + x^{-1}} dx$. We can rewrite the integral as: $I = \int e^{x + x^{-1}} dx + \int (x - x^{-1}) e^{x + x^{-1}} dx$. Using integration by parts on the first term $\int e^{x + x^{-1}} dx$: Let $u = x$ and $dv = e^{x + x^{-1}} dx$. This is not straightforward. Instead, consider the derivative of $x e^{x + x^{-1}}$: $\frac{d}{dx} (x e^{x + x^{-1}}) = 1 \cdot e^{x + x^{-1}} + x \cdot e^{x + x^{-1}} \cdot (1 - x^{-2}) = e^{x + x^{-1}} + x e^{x + x^{-1}} - x^{-1} e^{x + x^{-1}} = (1 + x - x^{-1}) e^{x + x^{-1}}$. Therefore, $\int (1 + x - x^{-1}) e^{x + x^{-1}} dx = x e^{x + x^{-1}} + C$.

$\int\left(1+x-x^{-1}\right) e^{x+x^{-1}} d x$ is equal to :

Similar Questions

If $\int(x^6+x^4+x^2) \sqrt{2x^4+3x^2+6} dx = f(x) + c$,then $f(3) =$

If $\int \frac{2 x^{12}+5 x^9}{\left(1+x^3+x^5\right)^3} d x=\frac{x^m}{l\left(1+x^3+x^5\right)^r}+C$ then $\frac{m-l}{r}=$

$\int \sqrt{3-2x-x^2} \, dx = $ . . . . . . $+ C$.

$\int \sec x \tan^3 x \, dx = $

If $\tan \alpha = \frac{4}{3}$, then $\int \frac{1}{3 \cos x - 4 \sin x} dx = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module