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

Step-by-step Solution

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Final Answer

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

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Rewrite the expression $\frac{x}{x^2+2x+1}$ inside the integral in factored form

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

Learn how to solve sum rule of differentiation problems step by step online.

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

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Learn how to solve sum rule of differentiation problems step by step online. Find the integral int(x/(x^2+2x+1))dx. Rewrite the expression \frac{x}{x^2+2x+1} inside the integral in factored form. Rewrite the fraction \frac{x}{\left(x+1\right)^{2}} 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 \left(x+1\right)^{2}. Multiplying polynomials.

Final Answer

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

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 (x/(x^2+2x))dx using partial fractionsSolve integral of (x/(x^2+2x))dx using basic integralsSolve integral of (x/(x^2+2x))dx using u-substitutionSolve integral of (x/(x^2+2x))dx using integration by partsSolve integral of (x/(x^2+2x))dx 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

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