👉 Try now NerdPal! Our new math app on iOS and Android

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

Step-by-step Solution

Go!
Math mode
Text mode
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

Final Answer

$-\frac{7}{2}$
Got another answer? Verify it here!

Step-by-step Solution

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 problems step by step online.

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

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve 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

$-\frac{7}{2}$

Exact Numeric Answer

$-3.5$

Explore different ways to solve this problem

Give us your feedback!

Function Plot

Plotting: $\frac{x^2-1}{x-1}$

SnapXam A2
Answer Assistant

beta
Got a different 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

How to improve your answer:

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account