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# Integrate the function $\frac{1}{x\left(x+1\right)}$ from $1$ to $2$

## Step-by-step Solution

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###  Videos

$0.287682$
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##  Step-by-step Solution 

Problem to solve:

$\int_{1}^{2}\frac{1}{x\cdot\left(x+1\right)}dx$

Specify the solving method

1

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

$\frac{1}{x\left(x+1\right)}=\frac{A}{x}+\frac{B}{x+1}$
2

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 $x\left(x+1\right)$

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

Learn how to solve definite integrals problems step by step online.

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

Learn how to solve definite integrals problems step by step online. Integrate the function 1/(x(x+1)) from 1 to 2. Rewrite the fraction \frac{1}{x\left(x+1\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 x\left(x+1\right). Multiplying polynomials. Simplifying.

$0.287682$

##  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 int(1/(x(x+1)))dx&1&2 using partial fractionsSolve int(1/(x(x+1)))dx&1&2 using basic integralsSolve int(1/(x(x+1)))dx&1&2 using u-substitutionSolve int(1/(x(x+1)))dx&1&2 using integration by partsSolve int(1/(x(x+1)))dx&1&2 using trigonometric substitution
SnapXam A2

### beta Got a different answer? Verify it!

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0
a
b
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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

$\int_{1}^{2}\frac{1}{x\cdot\left(x+1\right)}dx$

### Main topic:

Definite Integrals

~ 0.07 s