I encountered the following integral and I am bewildered:
$\displaystyle \int\frac{x^5-2x^4+3}{x^3-3x^2-10x}dx$
Seems to be real hard.
Hello, totalnewbie!
$\displaystyle \int\frac{x^5-2x^4+3}{x^3-3x^2-10x}dx$
Note that the numerator is of a higher degree than the denominator.
$\displaystyle \text{Long division: }\frac{x^5-2x^4+3}{x^3-3x^2-10x}\;=\;x^2+x+13 + \underbrace{\frac{49x^2+130x + 3}{x(x-5)(x+2)}}_{\text{use Partial Fractions}} $