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Intregal of sqrt(x + sqrt(x 2 + 1))dx. Please solve it as soon as possible.

Intregal of sqrt(x + sqrt(x2 + 1))dx. 
Please solve it as soon as possible.

Grade:11

1 Answers

Aditya Gupta
2081 Points
3 years ago
put y= x + sqrt(x2 + 1)
or y – x= sqrt(x2 + 1)
y^2+x^2 – 2xy= x2 + 1
or x= (y – 1/y)/2
so dx= (1+1/y^2)/2 dy
so integral becomes 
sqrt(y)(1+1/y^2)/2 dy
= ½*(y^1/2+y^-3/2)dy, which can easily be integrated.
kindly approve :)

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