Try NerdPal! Our new app on iOS and Android
Calculators Topics Solving Methods Step Reviewer Go Premium
ENG • ESP
Topics

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

Step-by-step Solution

Go!
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

$0.287682$
Got another answer? Verify it here!

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.

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

Unlock this complete solution and much more!

As low as $3.97 USD / week. Cancel anytime.

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.

Final Answer

$0.287682$

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
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

Evaluate the integral

$\int_0^{\infty}\left(\frac{1}{1+x^2}\right)dx$

Evaluate the integral

$\int_{1}^{3}\cos\left(x\right)^2dx$

Evaluate the integral

$\int_{-5}^{5}\frac{1}{\sqrt{5-x}}dx$

Evaluate the integral

$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$

Evaluate the integral

$\int_{2}^{4}\left(x^2+5x+6\right)dx$

Evaluate the integral

$\int_{2}^{5}\frac{1}{\left(x-1\right)\left(x+2\right)}dx$

Evaluate the integral

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

Main topic:

Definite Integrals

Used formulas:

3. See formulas

Time to solve it:

~ 0.07 s

Related topics:

Definite IntegralsIntegral CalculusCalculusIntegrals by Partial Fraction ExpansionMatricesGaussian Elimination

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?