Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $-x^2+2x+1$ by $4x-3$
Learn how to solve problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}4x\phantom{;}-3;}{-\frac{1}{4}x\phantom{;}+\frac{5}{16}\phantom{;}\phantom{;}}\\\phantom{;}4x\phantom{;}-3\overline{\smash{)}-x^{2}+2x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x\phantom{;}-3;}\underline{\phantom{;}x^{2}-\frac{3}{4}x\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{2}-\frac{3}{4}x\phantom{;};}\phantom{;}\frac{5}{4}x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}-3-;x^n;}\underline{-\frac{5}{4}x\phantom{;}+\frac{15}{16}\phantom{;}\phantom{;}}\\\phantom{;-\frac{5}{4}x\phantom{;}+\frac{15}{16}\phantom{;}\phantom{;}-;x^n;}\phantom{;}\frac{31}{16}\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Find the integral int((-x^2+2x+1)/(4x-3))dx. Divide -x^2+2x+1 by 4x-3. Resulting polynomial. Expand the integral \int\left(-\frac{1}{4}x+\frac{5}{16}+\frac{31}{16\left(4x-3\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{31}{16\left(4x-3\right)}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 4x-3 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.