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Integrate the function $\frac{x^2-1}{x-1}$ from $3$ to $2$

Step-by-step Solution

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Final Answer

$-\frac{7}{2}$
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Step-by-step Solution

Problem to solve:

$\int_{3}^{2}\frac{x^2-1}{x-1}dx$

Specify the solving method

1

Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: $\int_a^bf(x)dx=-\int_b^af(x)dx$

$-\int_{2}^{3}\frac{x^2-1}{x-1}dx$

Learn how to solve definite integrals problems step by step online.

$-\int_{2}^{3}\frac{x^2-1}{x-1}dx$

Unlock the first 2 steps of this solution!

Learn how to solve definite integrals problems step by step online. Integrate the function (x^2-1)/(x-1) from 3 to 2. Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: \int_a^bf(x)dx=-\int_b^af(x)dx. Rewrite the expression \frac{x^2-1}{x-1} inside the integral in factored form. Expand the integral \int\left(x+1\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral of a constant is equal to the constant times the integral's variable.

Final Answer

$-\frac{7}{2}$
SnapXam A2
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Got another 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
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

Useful tips on how to improve your answer:

$\int_{3}^{2}\frac{x^2-1}{x-1}dx$

Main topic:

Definite Integrals

Used formulas:

3. See formulas

Time to solve it:

~ 0.1 s