Find the integral $\int\left(x^7+x^5+x^3\right)\left(e^{3x}+e^{2x}+e^x\right)dx$

Used Formulas

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e
π
ln
log
log
lim
d/dx
Dx
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θ
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>
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>=
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sin
cos
tan
cot
sec
csc

asin
acos
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acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Basic Integrals

$\int e^xdx=e^x+C$
· Constant factor Rule
$\int cxdx=c\int xdx$

Integration Techniques

· Integration by Parts
$\int udv=uv - \int vdu$

Function Plot

Plotting: $e^x\cdot x^{3}-6e^x+6xe^x-3x^{2}e^x+C_0$

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1
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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

How to improve your answer:

Main Topic: Tabular Integration

Tabular integration is a special technique to solve certain integrals by parts usually made up of two functions: one polynomial and the other transcendent, like the exponential function or the sine. The method consists of deriving the polynomial function several times (until it becomes zero), and integrating the transcendent function several times. This method is usually applied when both functions can be easily derived and integrated multiple times.

Used Formulas

See formulas (3)

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