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# Find the integral $\int\frac{x^2+x+3}{x-2}dx$

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##  Final answer to the problem

$\frac{1}{2}x^2+3x+9\ln\left|x-2\right|+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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1

Divide $x^2+x+3$ by $x-2$

$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{2}+x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}+2x\phantom{;};}\phantom{;}3x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-3x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;-3x\phantom{;}+6\phantom{;}\phantom{;}-;x^n;}\phantom{;}9\phantom{;}\phantom{;}\\\end{array}$

Learn how to solve problems step by step online.

$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{2}+x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}+2x\phantom{;};}\phantom{;}3x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-3x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;-3x\phantom{;}+6\phantom{;}\phantom{;}-;x^n;}\phantom{;}9\phantom{;}\phantom{;}\\\end{array}$

Learn how to solve problems step by step online. Find the integral int((x^2+x+3)/(x-2))dx. Divide x^2+x+3 by x-2. Resulting polynomial. Expand the integral \int\left(x+3+\frac{9}{x-2}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int xdx results in: \frac{1}{2}x^2.

##  Final answer to the problem

$\frac{1}{2}x^2+3x+9\ln\left|x-2\right|+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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1
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7
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9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch