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# Find the integral of $\frac{x^3+x+5}{x+1}$

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##  Final answer to the problem

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

How should I solve this problem?

• Find the integral
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Prove from LHS (left-hand side)
• Load more...
Can't find a method? Tell us so we can add it.
1

Find the integral

$\int\frac{x^3+x+5}{x+1}dx$

Learn how to solve integral calculus problems step by step online.

$\int\frac{x^3+x+5}{x+1}dx$

Learn how to solve integral calculus problems step by step online. Find the integral of (x^3+x+5)/(x+1). Find the integral. Divide x^3+x+5 by x+1. Resulting polynomial. Expand the integral \int\left(x^{2}-x+2+\frac{3}{x+1}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately.

##  Final answer to the problem

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

##  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
2
3
4
5
6
7
8
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

###  Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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