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intx^(51)(tan^(- 1)x+cot^(- 1)x)dx=...

`intx^(51)(tan^(- 1)x+cot^(- 1)x)dx=`

A

`(x^(52))/(52)(tan^(-1)x+cot^(-1)x)+C`

B

`(x^(52))/(52)(tan^(-1)x-cot^(-1)x)+C`

C

`(pix^(52))/(104)+(pi)/(2)+C`

D

`(x^(52))/(52)+(pi)/(2)+C`

Text Solution

Verified by Experts

The correct Answer is:
A
`intx^(51)(tan^(-1)x+cot^(-1)x)dx`
`=intx^(51).(pi)/(2)dx=(pix^(52))/(104)+C=(x^(52))/(52)(tan^(-1)x+cot^(-1)x)+C`
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