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i have integral $\int \frac{x^{5}+x+3}{x{^3}-5x^{2}}\mathrm dx$,

so first step is to divide polynoms, and i get:

$\frac{x^{5}+x+3}{x{^3}-5x^{2}}$ = $x^{2} + 5x + 25$ with remainder $125x^2 + x + 3$

is it corrent to divide this polynomial division into two integrals:

int 1: $\int x^{2}+5x+25 \mathrm dx$

int 2: $\int \frac{125x^{2}+x+3}{x{^2}(x-5)}\mathrm dx$

first integral solve directly from tables, and make partial fractions from second integral, then just merge solutions into one expression.

  • 2
    Yes. It is correct.2011-09-05

3 Answers 3