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

Used Formulas

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ln
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sin
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tan
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asin
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sinh
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tanh
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asinh
acosh
atanh
acoth
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Basic Derivatives

· Quotient Rule in Differentiation
$\frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}$
· Derivative of a Constant
$\frac{d}{dx}\left(c\right)=0$
· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Basic Integrals

· Integral of a Constant
$\int cdx=cvar+C$
· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$
· Constant factor Rule
$\int cxdx=c\int xdx$
· Power Rule of Integration
$\int x^ndx=\frac{x^{\left(n+1\right)}}{n+1}+C$

Integration Techniques

· Integration by Parts
$\int udv=uv - \int vdu$
· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$

Function Plot

Plotting: $\frac{x}{2x+1}+\frac{1}{2\left(2x+1\right)}+\frac{1}{2}\ln\left(2x+1\right)+C_0$

SnapXam A2
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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

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