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# Find the integral $\int\frac{1}{u\left(1+u\right)}du$

## Step-by-step Solution

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$\ln\left(u\right)-\ln\left(u+1\right)+C_0$
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##  Step-by-step Solution 

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Rewrite the fraction $\frac{1}{u\left(1+u\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{1}{u\left(1+u\right)}=\frac{A}{u}+\frac{B}{1+u}$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\frac{1}{u\left(1+u\right)}=\frac{A}{u}+\frac{B}{1+u}$

Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int(1/(u(1+u)))du. Rewrite the fraction \frac{1}{u\left(1+u\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by u\left(1+u\right). Multiplying polynomials. Simplifying.

$\ln\left(u\right)-\ln\left(u+1\right)+C_0$

##  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 (1/u(1+u))du using partial fractionsSolve integral of (1/u(1+u))du using basic integralsSolve integral of (1/u(1+u))du using u-substitutionSolve integral of (1/u(1+u))du using integration by partsSolve integral of (1/u(1+u))du using trigonometric substitution

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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

### Main Topic: Integrals by Partial Fraction Expansion

The partial fraction decomposition or partial fraction expansion of a rational function is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

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