Question

Solve the following

① xe* da​

Answer 1

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12th

>Maths

>Integrals

>Integration by Parts

>Evaluate int a^x e^x dx . ...

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Evaluate ∫a

x

e

x

dx.

Medium

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Answer

∫a

x

e

x

dx

⇒ Let I=∫a

x

e

x

dx

Here we use intergration by parts, ∫udv=uv−∫vdu

⇒I=a

x

e

x

−∫a

x

(lna) e

x

dx

⇒I=a

x

e

x

−lna∫a

x

e

x

dx

This can be written as

⇒I=a

x

e

x

−(lna)I

⇒(1+lna)I=a

x

e

x

⇒I=

1+lna

a

x

e

x

Therefore, ⇒∫a

x

e

x

dx=

1+lna

a

x

e

x