Contents of this Calculus 2 episode:

The T2 integration rule, Integrating fractions step by step, The numerator is derivative of the denominator.

T2

Let's see an example of this.

differentiate

Here comes another one:

Sometimes the numerator is not exactly the derivative of the denominator, but very similar.

In such cases, to draw inspiration, we differentiate the denominator, and compare it with the numerator to see what we should do to succeed.

There is, sadly only x in the numerator, while we would need 4x.

So, we multiply the numerator by 4, and in turn, we divide by 4 outside of the integral sign.

Having fewer x in the numerator can cause trouble, and so does having more.

.

The derivative of the denominator is , but in the numerator we have , which is more than we need, so we factor out a 3.

Finally, there are some very cunning cases, too.

There are some that are even trickier.

Calculus 2 episode