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# Find the integral $\int\frac{\left(x^2+1\right)^2+5}{x^2+1}dx$

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##  Final answer to the problem

$\frac{x^{3}}{3}+x+5\arctan\left(x\right)+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

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• 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

Expand the fraction $\frac{\left(x^2+1\right)^2+5}{x^2+1}$ into $2$ simpler fractions with common denominator $x^2+1$

$\int\left(\frac{\left(x^2+1\right)^2}{x^2+1}+\frac{5}{x^2+1}\right)dx$

Learn how to solve integrals of rational functions problems step by step online.

$\int\left(\frac{\left(x^2+1\right)^2}{x^2+1}+\frac{5}{x^2+1}\right)dx$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int(((x^2+1)^2+5)/(x^2+1))dx. Expand the fraction \frac{\left(x^2+1\right)^2+5}{x^2+1} into 2 simpler fractions with common denominator x^2+1. Simplify the resulting fractions. Expand the integral \int\left(x^2+1+\frac{5}{x^2+1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^2dx results in: \frac{x^{3}}{3}.

##  Final answer to the problem

$\frac{x^{3}}{3}+x+5\arctan\left(x\right)+C_0$

##  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

SnapXam A2

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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

###  Main Topic: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).