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Integrate the function $\frac{x^2-3}{\left(x+2\right)\left(x+1\right)^2}$ from 0 to $5$

Step-by-step Solution

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Final Answer

$-0.413904$
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Step-by-step Solution

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Rewrite the fraction $\frac{x^2-3}{\left(x+2\right)\left(x+1\right)^2}$ in $3$ simpler fractions using partial fraction decomposition

$\frac{x^2-3}{\left(x+2\right)\left(x+1\right)^2}=\frac{A}{x+2}+\frac{B}{\left(x+1\right)^2}+\frac{C}{x+1}$

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

$\frac{x^2-3}{\left(x+2\right)\left(x+1\right)^2}=\frac{A}{x+2}+\frac{B}{\left(x+1\right)^2}+\frac{C}{x+1}$

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Learn how to solve quotient rule of differentiation problems step by step online. Integrate the function (x^2-3)/((x+2)(x+1)^2) from 0 to 5. Rewrite the fraction \frac{x^2-3}{\left(x+2\right)\left(x+1\right)^2} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C. The first step is to multiply both sides of the equation from the previous step by \left(x+2\right)\left(x+1\right)^2. Multiply both sides of the equality by 1 to simplify the fractions. Multiplying polynomials.

Final Answer

$-0.413904$

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Function Plot

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

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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

How to improve your answer:

Main Topic: Quotient Rule of Differentiation

The quotient rule is a formal rule for differentiating problems where one function is divided by another.

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