Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $x^2+2x-1$ by $x-4$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-4;}{\phantom{;}x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-4\overline{\smash{)}\phantom{;}x^{2}+2x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-4;}\underline{-x^{2}+4x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}+4x\phantom{;};}\phantom{;}6x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n;}\underline{-6x\phantom{;}+24\phantom{;}\phantom{;}}\\\phantom{;-6x\phantom{;}+24\phantom{;}\phantom{;}-;x^n;}\phantom{;}23\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^2+2x+-1)/(x-4))dx. Divide x^2+2x-1 by x-4. Resulting polynomial. Expand the integral \int\left(x+6+\frac{23}{x-4}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{23}{x-4}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x-4 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.