∫ xe^x.dx Using ILATE, ∫xI.e^xII.dx Using by parts ∫ xe^x.dx = x ∫ e^x.dx ∫ nbsp; ( ddx(x)∫ e^x.dx ).dx = xe^x ∫ 1.e^x.dx =xe^x e^x+ C Where C is const ...

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Standard XII

Mathematics

Logarithmic Differentiation

Find : ∫ xex....

Question

Find : $\int x e^{x} . d x$

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Solution

$\int x e^{x} . d x$
Using ILATE,
$\int x    I . e^{x}    I I . d x$
Using by parts
$\int x e^{x} . d x$
$= x \int e^{x} . d x - \int (\frac{d}{d x} (x) \int e^{x} . d x) . d x$
$= x e^{x} - \int 1. e^{x} . d x$
$= x e^{x} - e^{x} + C$
Where $C$ is constant of integration.

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Logarithmic Differentiation

Standard XII Mathematics

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Find : ∫xex.dx

∫xex.dx Using ILATE, ∫xI.exII.dx Using by parts ∫xex.dx =x∫ex.dx−∫(ddx(x)∫ex.dx).dx =xex−∫1.ex.dx =xex−ex+C Where C is constant of integration.

Find : $\int x e^{x} . d x$

$\int x e^{x} . d x$
Using ILATE,
$\int x    I . e^{x}    I I . d x$
Using by parts
$\int x e^{x} . d x$
$= x \int e^{x} . d x - \int (\frac{d}{d x} (x) \int e^{x} . d x) . d x$
$= x e^{x} - \int 1. e^{x} . d x$
$= x e^{x} - e^{x} + C$
Where $C$ is constant of integration.