u-প্রতিস্থাপনের কৌশল

U-substitution is a method for integrating that makes the process much easier.

Say we nee to evaluate $\int\frac{4x^3}{x^4+7}dx$

What we want to do is set $u$ equal to the part of the function which we have the derivative of also in the function. Here we would set $u$ equal to $x^4+7$ because the derivative of $x^4+7$ is $4x^3$. This will make things easier down the line.

Now we know that $u=x^4+7$ and $du=4x^3\,dx$ so we can rewrite the original function in terms of $u$.

Once we have the function in terms of $u$ it is much easier to see what the integral is.

Now all we need to do is plug $u$ back into the function.

$\ln(x^4+7)+C$