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Let us consider the integral of the foll...

Let us consider the integral of the following forms
`f(x_(1), sqrt(mx^(2)+nx+p))^(1//2)`
Case I If `m gt 0`, then put `sqrt(mx^(2)+nx+C)=u pm x sqrt(m)`
Case II If `p gt 0`, then put `sqrt(mx^(2)+nx+C)=u x pm sqrt(p)`
Case III If quadratic equation `mx^(2)+nx+p=0` has real roots `alpha` and `beta` there put `sqrt(mx^(2)+nx+p)=(x-alpha) u ` or `(x-beta)u`
`int ((x+sqrt(1+x^(2)))^(15))/(sqrt(1+x^(2))) dx` is equal to

A

`((x+sqrt(1+x^(2)))^(16))/(10)+c`

B

`(1)/(15(sqrt(1+x^(2)+x)))+c`

C

`(15)/(sqrt(1+x^(2))+x)+`c

D

`((sqrt(1+x^(2))+x))/(15)+c`

Text Solution

Verified by Experts

The correct Answer is:
D
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