Integrating by parts (with v = x and du/dx=e^ x), we get: xe^ x ∫ e^ x dx (since ∫ e^ x dx= e^ x) = xe^ x e^ x+constant We can also sometime use integration ...

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Byju's Answer

Standard XII

Mathematics

Integration by Partial Fractions

Find ∫ xe - x...

Question

Find $\int x e^{- x} d x$

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Solution

Integrating by parts (with v = x and $\frac{d u}{d x} = e^{- x}$ ), we get:
$- x e^{- x} - \int - e^{- x} d x$ (since $\int e^{- x} d x = - e^{- x}$ )
$= - x e^{- x} - e^{- x} + c o n s t a n t$
We can also sometime use integration by parts when we want to integrate a function that cannot be split into the product of two things. The trick we use in such circumstances is to multiply by 1 and take $\frac{d u}{d x} = 1$

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\int \sqrt{x} e^{\sqrt{X}} d x =

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(a) − xe^x + C

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Find ∫xe−x dx

Find $\int x e^{- x} d x$