Integrating by parts

1. Mar 19, 2013

Aerospace93

1. The problem statement, all variables and given/known data
∫arctan(√x)dx.

Using the substitution √x=t:
∫arctan(√x)dx = ∫arctan(t)dt2

This is what ive got written in a solution manual. I dont see why the dt would be squared. Could anyone care explaining me? thanks

2. Mar 19, 2013

HallsofIvy

The substitution $t= \sqrt{x}$ is the same (for positive x and t) as $t^2= x$ so that $dx= d(t^2)= 2tdt$.

What is done here is "integration by substitution". The result is $2\int arctan(t) tdt$ which can now be done by "integration by parts".

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