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

Step-by-step Solution

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Solution

Final Answer

$\frac{-1}{-2\left(x+1\right)^{2}}+\frac{2}{9}\ln\left(x-2\right)-\frac{1}{3}\ln\left(x+1\right)+\frac{-5}{9\left(x+1\right)}+C_0$
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Step-by-step Solution

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When multiplying exponents with same base you can add the exponents: $\left(x+1\right)^2\left(x+1\right)\left(x-2\right)$

$\int\frac{x^2+2}{\left(x+1\right)^{3}\left(x-2\right)}dx$

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$\int\frac{x^2+2}{\left(x+1\right)^{3}\left(x-2\right)}dx$

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Learn how to solve problems step by step online. Find the integral int((x^2+2)/((x+1)^2(x+1)(x-2)))dx. When multiplying exponents with same base you can add the exponents: \left(x+1\right)^2\left(x+1\right)\left(x-2\right). Rewrite the fraction \frac{x^2+2}{\left(x+1\right)^{3}\left(x-2\right)} in 4 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C, D. The first step is to multiply both sides of the equation from the previous step by \left(x+1\right)^{3}\left(x-2\right). Multiplying polynomials.

Final Answer

$\frac{-1}{-2\left(x+1\right)^{2}}+\frac{2}{9}\ln\left(x-2\right)-\frac{1}{3}\ln\left(x+1\right)+\frac{-5}{9\left(x+1\right)}+C_0$

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 ((x^2+2)/(x+1)^2(x+1))dx using partial fractionsSolve integral of ((x^2+2)/(x+1)^2(x+1))dx using basic integralsSolve integral of ((x^2+2)/(x+1)^2(x+1))dx using u-substitutionSolve integral of ((x^2+2)/(x+1)^2(x+1))dx using integration by partsSolve integral of ((x^2+2)/(x+1)^2(x+1))dx using trigonometric substitution

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Function Plot

Plotting: $\frac{-1}{-2\left(x+1\right)^{2}}+\frac{2}{9}\ln\left(x-2\right)-\frac{1}{3}\ln\left(x+1\right)+\frac{-5}{9\left(x+1\right)}+C_0$

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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

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