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# Find the integral $\int y^2e^{2y}dy$

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##  Final answer to the problem

$\frac{1}{2}y^2e^{2y}-\frac{1}{2}ye^{2y}+\frac{1}{4}e^{2y}+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Integrate by trigonometric substitution
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
• FOIL Method
Can't find a method? Tell us so we can add it.
1

We can solve the integral $\int y^2e^{2y}dy$ by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form $\int P(x)T(x) dx$. $P(x)$ is typically a polynomial function and $T(x)$ is a transcendent function such as $\sin(x)$, $\cos(x)$ and $e^x$. The first step is to choose functions $P(x)$ and $T(x)$

$\begin{matrix}P(x)=y^2 \\ T(x)=e^{2y}\end{matrix}$

Learn how to solve integrals of exponential functions problems step by step online.

$\begin{matrix}P(x)=y^2 \\ T(x)=e^{2y}\end{matrix}$

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(y^2e^(2y))dy. We can solve the integral \int y^2e^{2y}dy by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x). Derive P(x) until it becomes 0. Integrate T(x) as many times as we have had to derive P(x), so we must integrate e^{2y} a total of 3 times. With the derivatives and integrals of both functions we build the following table.

##  Final answer to the problem

$\frac{1}{2}y^2e^{2y}-\frac{1}{2}ye^{2y}+\frac{1}{4}e^{2y}+C_0$

##  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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7
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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: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.