Help me to integrate w/o knowing the function

Recently, I faced a problem to solve this integral

$\int { xdy+ydx }$

without any function $y=f\left( x \right)$ . A friend of mine helped me here. He told me to substitute $xy=t$ so that $xdy+ydx$ becomes $dt$ and the integral gets evaluated to $xy$

Now I want to know more about this technique in calculus.

What this technique is known as?

Do we have a wiki about it here on Brilliant?

P.S.:I was totally awestruck when I solved this integral without knowing the function

#Calculus #DifferentialEquations

Easy Math Editor

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Comments

This is a simple Integration By parts question
$\int{x dy} + \int{y dx} \\ \text{Integrating by parts we get} \\ x \int{dy} - \int{y dx} + \int {y dx} \\ = \boxed{xy}$

Wiki

Rajdeep Dhingra - 6 years, 2 months ago

nice!