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Integrate the function $\frac{x^2+2x-6}{x^3-x}$ from $2$ to $4$

Step-by-step Solution

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Final Answer

$\frac{47}{65}$
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Step-by-step Solution

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Rewrite the expression $\frac{x^2+2x-6}{x^3-x}$ inside the integral in factored form

$\int_{2}^{4}\frac{x^2+2x-6}{x\left(x+1\right)\left(x-1\right)}dx$

Learn how to solve differential calculus problems step by step online.

$\int_{2}^{4}\frac{x^2+2x-6}{x\left(x+1\right)\left(x-1\right)}dx$

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Learn how to solve differential calculus problems step by step online. Integrate the function (x^2+2x+-6)/(x^3-x) from 2 to 4. Rewrite the expression \frac{x^2+2x-6}{x^3-x} inside the integral in factored form. Rewrite the fraction \frac{x^2+2x-6}{x\left(x+1\right)\left(x-1\right)} 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 x\left(x+1\right)\left(x-1\right). Multiply both sides of the equality by 1 to simplify the fractions.

Final Answer

$\frac{47}{65}$

Exact Numeric Answer

$0.7231$

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Function Plot

Plotting: $\frac{x^2+2x-6}{x^3-x}$

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2
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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
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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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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