Final Answer
$\frac{x^{3}}{3}-4x^2+66x+543\ln\left(\frac{3\sqrt{2}}{\sqrt{-18+\left(x+4\right)^2}}\right)-271.646855\ln\left(8.242641+x\right)+271.646855\ln\left(-\frac{33}{136}+x\right)+C_0$
Got another answer? Verify it here!
Step-by-step Solution
Specify the solving method
Choose an option Integrals by Partial Fraction Expansion Basic Integrals Integration by Substitution Integration by Parts Integration by Trigonometric Substitution Suggest another method or feature
Send
1
Divide $x^4+x+1$ by $x^2+8x-2$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+8x\phantom{;}-2;}{\phantom{;}x^{2}-8x\phantom{;}+66\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+8x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}+x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+8x\phantom{;}-2;}\underline{-x^{4}-8x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-8x^{3}+2x^{2};}-8x^{3}+2x^{2}+x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+8x\phantom{;}-2-;x^n;}\underline{\phantom{;}8x^{3}+64x^{2}-16x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}8x^{3}+64x^{2}-16x\phantom{;}-;x^n;}\phantom{;}66x^{2}-15x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+8x\phantom{;}-2-;x^n-;x^n;}\underline{-66x^{2}-528x\phantom{;}+132\phantom{;}\phantom{;}}\\\phantom{;;-66x^{2}-528x\phantom{;}+132\phantom{;}\phantom{;}-;x^n-;x^n;}-543x\phantom{;}+133\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{2}+8x\phantom{;}-2;}{\phantom{;}x^{2}-8x\phantom{;}+66\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+8x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}+x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+8x\phantom{;}-2;}\underline{-x^{4}-8x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-8x^{3}+2x^{2};}-8x^{3}+2x^{2}+x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+8x\phantom{;}-2-;x^n;}\underline{\phantom{;}8x^{3}+64x^{2}-16x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}8x^{3}+64x^{2}-16x\phantom{;}-;x^n;}\phantom{;}66x^{2}-15x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+8x\phantom{;}-2-;x^n-;x^n;}\underline{-66x^{2}-528x\phantom{;}+132\phantom{;}\phantom{;}}\\\phantom{;;-66x^{2}-528x\phantom{;}+132\phantom{;}\phantom{;}-;x^n-;x^n;}-543x\phantom{;}+133\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^4+x+1)/(x^2+8x+-2))dx. Divide x^4+x+1 by x^2+8x-2. Resulting polynomial. Expand the integral \int\left(x^{2}-8x+66+\frac{-543x+133}{x^2+8x-2}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{2}dx results in: \frac{x^{3}}{3}.
Final Answer
$\frac{x^{3}}{3}-4x^2+66x+543\ln\left(\frac{3\sqrt{2}}{\sqrt{-18+\left(x+4\right)^2}}\right)-271.646855\ln\left(8.242641+x\right)+271.646855\ln\left(-\frac{33}{136}+x\right)+C_0$