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# Find the integral $\int\frac{x^2}{x+1}dx+\int\frac{y}{y+2}dy$

## Step-by-step Solution

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Solving: $\int\frac{x^2}{x+1}dx+\int\frac{y}{y+2}dy$

##  Final answer to the problem

$\ln\left|x+1\right|-x+\frac{1}{2}x^2-2\ln\left|y+2\right|+y+C_1$
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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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The integral $\int\frac{x^2}{x+1}dx$ results in: $\frac{1}{2}x^2-x+\ln\left|x+1\right|$

$\frac{1}{2}x^2-x+\ln\left|x+1\right|$

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

$\frac{1}{2}x^2-x+\ln\left|x+1\right|$

Learn how to solve integral calculus problems step by step online. Find the integral int((x^2)/(x+1))dx+int(y/(y+2))dy. The integral \int\frac{x^2}{x+1}dx results in: \frac{1}{2}x^2-x+\ln\left|x+1\right|. Gather the results of all integrals. The integral \int\frac{y}{y+2}dy results in: y+2-2\ln\left|y+2\right|. Gather the results of all integrals.

##  Final answer to the problem

$\ln\left|x+1\right|-x+\frac{1}{2}x^2-2\ln\left|y+2\right|+y+C_1$

##  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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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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.