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int(sinx-cosx)^(4)(sinx+cosx)dx is equal...

`int(sinx-cosx)^(4)(sinx+cosx)dx` is equal to

A

`(sin x - cosx)/(5)+C`

B

`((sin x - cosx)^(5))/(5)+C`

C

`((sin x-cosx)^(4))/(4)+C`

D

`((sinx+cosx)^(5))/(5)+C`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=int(sinx-cosx)^(4)(sinx +cosx)dx`
Put`" "Sinx-cosx=t`
`rArr" "(cos x+sin x)dx=dt`
`therefore" "l=int t^(4)dt=(t^(5))/(5)+C=((sinx-cosx)^(5))/(5)+C`
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