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# Find the integral of $\frac{x^3+x-1}{x^4+6x^2+9}$

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##  Final answer to the problem

$-\ln\left(\frac{\sqrt{3}}{\sqrt{x^{2}+3}}\right)-\frac{1}{6\sqrt{3}}\arctan\left(\frac{x}{\sqrt{3}}\right)+\frac{-x}{6\left(x^{2}+3\right)}+\frac{1}{x^{2}+3}+C_0$
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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)
Can't find a method? Tell us so we can add it.
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Find the integral

$\int\frac{x^3+x-1}{x^4+6x^2+9}dx$

Learn how to solve problems step by step online.

$\int\frac{x^3+x-1}{x^4+6x^2+9}dx$

Learn how to solve problems step by step online. Find the integral of (x^3+x+-1)/(x^4+6x^2+9). Find the integral. The trinomial x^4+6x^2+9 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial.

##  Final answer to the problem

$-\ln\left(\frac{\sqrt{3}}{\sqrt{x^{2}+3}}\right)-\frac{1}{6\sqrt{3}}\arctan\left(\frac{x}{\sqrt{3}}\right)+\frac{-x}{6\left(x^{2}+3\right)}+\frac{1}{x^{2}+3}+C_0$

##  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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9
0
a
b
c
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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