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# Integrate the function $\frac{x^2}{x+1}$ from $9$ to $4$

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##  Final answer to the problem

$-\frac{65}{2}-\ln\left(10\right)$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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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: $\int_a^bf(x)dx=-\int_b^af(x)dx$

$-\int_{4}^{9}\frac{x^2}{x+1}dx$

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

$-\int_{4}^{9}\frac{x^2}{x+1}dx$

Learn how to solve definite integrals problems step by step online. Integrate the function (x^2)/(x+1) from 9 to 4. 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. Divide x^2 by x+1. Resulting polynomial. Expand the integral \int\left(x-1+\frac{1}{x+1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.

##  Final answer to the problem

$-\frac{65}{2}-\ln\left(10\right)$

##  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

SnapXam A2

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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

###  Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b