Integration (2 Viewers)

[pikachu975]

Thank you for the help as well as Drongoski and BenHowe

 

[BenHowe]

How did you write the quotient and remainder part underneath the terms, it looks so epic

 

[BenHowe]

Pikachu the only reason I said that you mighta thought it had the square root in the denominator because originally I thought it did as well and got the same answer as you

 

[InteGrand]

How did you write the quotient and remainder part underneath the terms, it looks so epic

I used

\underbrace{...}_{\text{...}}

.

(Replace the first "..." with the thing you want the brace to go under and the second "..." with what text you want to write under the brace.)

 

[pikachu975]

Pikachu the only reason I said that you mighta thought it had the square root in the denominator because originally I thought it did as well and got the same answer as you

I checked I didn't have it, I used integrand's method stated somewhere above

 

[pikachu975]

Note that in your previous one where I added and subtracted something to get the numerator of lower degree than the denominator was actually just a shortcut method of polynomial division. (So even if the numerator has equal degree to the denominator, we need to divide first so that the numerator degree becomes strictly less than the denominator degree, after which we can use the earlier outlined method.)

Also note that if the denominator is a quadratic (without square root) with two easy roots and the numerator is a linear function (including constant function), we can also use the method of partial fractions relatively easily.

What if the degree is the same but there is a square root on the bottom?

 

[BenHowe]

Prolly a trig substitution if x^2 sorta thing. A subsitution will also work well