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LetIn= int tan^nx dx, (n>1). If I4+I6=at...

Let`I_n= int tan^nx dx`, `(n>1)`. If `I_4+I_6=atan^5x+bx^5+c` where c is a constant of integration then thee ordered pair (a,b) is

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

`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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