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Find the integral $\int\frac{2u-1}{4u^2-1}du$

Step-by-step Solution

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Solving: $\int\frac{2u-1}{4u^2-1}du$
Solve instead: $\int\frac{2u-1}{4u^2-1}dt$

Solution

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Final Answer

$\frac{1}{2}\ln\left(2u+1\right)+C_0$
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Step-by-step Solution

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Expand the fraction $\frac{2u-1}{4u^2-1}$ into $2$ simpler fractions with common denominator $4u^2-1$

$\int\left(\frac{2u}{4u^2-1}+\frac{-1}{4u^2-1}\right)du$

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

$\int\left(\frac{2u}{4u^2-1}+\frac{-1}{4u^2-1}\right)du$

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int((2u-1)/(4u^2-1))du. Expand the fraction \frac{2u-1}{4u^2-1} into 2 simpler fractions with common denominator 4u^2-1. Simplify the expression inside the integral. The integral 2\int\frac{u}{4u^2-1}du results in: \frac{1}{4}\ln\left(2u+1\right)+\frac{1}{4}\ln\left(2u-1\right). Gather the results of all integrals.

Final Answer

$\frac{1}{2}\ln\left(2u+1\right)+C_0$

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

Solve integral of ((2u-1)/(4u^2-1))du using partial fractionsSolve integral of ((2u-1)/(4u^2-1))du using basic integralsSolve integral of ((2u-1)/(4u^2-1))du using u-substitutionSolve integral of ((2u-1)/(4u^2-1))du using integration by partsSolve integral of ((2u-1)/(4u^2-1))du using trigonometric substitution

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Function Plot

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

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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
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

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Main Topic: Integrals of Rational Functions

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

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2. See formulas

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