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If l(n)=intx^(n).e^(cx)dx for n ge 1, th...

If `l_(n)=intx^(n).e^(cx)dx` for `n ge 1`, then `C.l_(n)+n.l_(n-1)` is equal to

A

`x^(n)e^(cx)`

B

`x^(n)`

C

`e^(cx)`

D

`x^(n)+e^(cx)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `l_(n)=int x^(n).e^(cx)dx=x^(n).(e^(cx))/(c)-int nx^(n-1).(e^(cx))/(c)dx`
`rArr" "l_(n)=(e^(cx).x^(n))/(c)-(n)/(c)l_(n-1)`
`rArr" "cl_(n)+nl_(n-1)=e^(cx).x^(n)`
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