First slide

Methods of integration

Question

$\int (1 + x - x^{- 1}) e^{x + x^{- 1}} d x =$

Moderate

A

$(x + 1) e^{x + x^{- 1}} + c$
B

$(x - 1) e^{x + x^{- 1}} + c$
C

$\frac{1}{2} x e^{x + x^{- 1}} + c$
D

$x . e^{x + x^{- 1}} + c$

Solution

$\int e^{x + x^{- 1}} (1 + x - x^{- 1}) d x$
$= \int [x [1 - \frac{1}{x^{2}}] + 1] e^{x + x^{- 1}} d x (\sin c e \int e^{f (x)} [f^{'} (x) g (x) + g^{'} (x)] d x = e^{f (x)} g (x))$
$= x e^{x + x^{- 1}} + c$

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