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Let In=int tan^n x dx, (n>1). If I4+I6...

Let `I_n=int tan^n x dx, (n>1)`. If `I_4+I_6=a tan^5 x + bx^5 + C`, Where `C` is a constant of integration, then the ordered pair `(a,b)` is equal to :

A

`(-(1)/(5),0)`

B

`(-(1)/(5),1)`

C

`((1)/(5),0)`

D

`((1)/(5),-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
`I_(n)=int tan^(n)x dx`
` I_(4)+I_(6)=int(tan^(4)x+tan^(6)x)dx`
`=int tan^(4)xsec^(2)xdx`
`=(1)/(5) tan^(5)x+C`
` :. atan^(5)x+bx^(5)+C=(1)/(5)tan^(5)x+C ("given")`
`a=(1)/(5),b=0`
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