👉 Try now NerdPal! Our new math app on iOS and Android
Calculators Topics Solving Methods Step Checker
Book solutions
Algebra Baldor
Go Premium Topics

Find the integral $\int\frac{x^2+1}{x^2+x+1}dx$

Step-by-step Solution

Go!
Math mode
Text mode
Go!
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
D□x
∫
∫◻
|◻|
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

Solution

Formulas

Videos

Final Answer

$x+\frac{\sqrt{3}}{3}\arctan\left(1.154696\left(x+\frac{1}{2}\right)\right)+\frac{1}{\log^{3}\left(10\right)}\ln\left(\frac{\frac{\sqrt{3}}{2}}{\sqrt{\frac{3}{4}+\left(x+\frac{1}{2}\right)^2}}\right)+C_0$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

Divide $x^2+1$ by $x^2+x+1$

$\begin{array}{l}\phantom{\phantom{;}x^{2}+x\phantom{;}+1;}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+1;}\underline{-x^{2}-x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{-x^{2}-x\phantom{;}-1\phantom{;}\phantom{;};}-x\phantom{;}\phantom{-;x^n}\\\end{array}$

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

$\begin{array}{l}\phantom{\phantom{;}x^{2}+x\phantom{;}+1;}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+1;}\underline{-x^{2}-x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{-x^{2}-x\phantom{;}-1\phantom{;}\phantom{;};}-x\phantom{;}\phantom{-;x^n}\\\end{array}$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^2+1)/(x^2+x+1))dx. Divide x^2+1 by x^2+x+1. Resulting polynomial. Simplify the expression inside the integral. The integral \int1dx results in: x.

Final Answer

$x+\frac{\sqrt{3}}{3}\arctan\left(1.154696\left(x+\frac{1}{2}\right)\right)+\frac{1}{\log^{3}\left(10\right)}\ln\left(\frac{\frac{\sqrt{3}}{2}}{\sqrt{\frac{3}{4}+\left(x+\frac{1}{2}\right)^2}}\right)+C_0$

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

Solve integral of ((x^2+1)/(x^2+x))dx using partial fractionsSolve integral of ((x^2+1)/(x^2+x))dx using basic integralsSolve integral of ((x^2+1)/(x^2+x))dx using u-substitutionSolve integral of ((x^2+1)/(x^2+x))dx using integration by partsSolve integral of ((x^2+1)/(x^2+x))dx using trigonometric substitution

Give us your feedback!

Function Plot

Plotting: $x+\frac{\sqrt{3}}{3}\arctan\left(1.154696\left(x+\frac{1}{2}\right)\right)+\frac{1}{\log^{3}\left(10\right)}\ln\left(\frac{\frac{\sqrt{3}}{2}}{\sqrt{\frac{3}{4}+\left(x+\frac{1}{2}\right)^2}}\right)+C_0$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
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
D□x
∫
∫◻
|◻|
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

How to improve your answer:

Similar Problems Solved

Compute the integral

$\int\frac{x}{\sqrt{x^2+9}}dx$

Compute the integral

$\int\frac{dx}{x^2\sqrt{4-x^2}}$

Compute the integral

$\int\frac{1}{\sqrt{x^2-36}}dx$

Compute the integral

$\int\frac{1}{\sqrt{1-x^2}}dx$

Compute the integral

$\int\frac{x}{\sqrt{16-x^2}}dx$

Compute the integral

$\int\frac{1}{\sqrt{1-5x}}dx$

Compute the integral

$\int\frac{x^3}{\sqrt{x^2+4}}dx$

Main Topic: Integrals of Rational Functions

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

Used Formulas

4. See formulas

Related Topics

Supercharge your math learning

By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot password?

Supercharge your math learning



Register here if you don't have an account.
Forgot password?

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account