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Find the integral $\int x^3\sin\left(2x\right)dx$

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Solution

Formulas

Videos

Integration By Parts - Tabular Method

https://www.youtube.com/watch?v=Yyic5aaXGaw

Calculus - Find the derivative of natural logarithm using product property, d(ln(2x))/dx

https://www.youtube.com/watch?v=urYZhqwUTI0

Integral of tan^5x

https://www.youtube.com/watch?v=-2Q7MSyYo70

Integral of 1/sqrt(1-x^2)

https://www.youtube.com/watch?v=9AvyXgfNN9E

integral of arcsin x

https://www.youtube.com/watch?v=qwHhwdvTGdY

Integral of Sin(lnx)

https://www.youtube.com/watch?v=r2zyTfXyYMc

Function Plot

Plotting: $-\frac{1}{2}x^3\cos\left(2x\right)+\frac{3}{4}x^{2}\sin\left(2x\right)+\frac{3}{4}x\cos\left(2x\right)-\frac{3}{8}\sin\left(2x\right)+C_0$

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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
D□x
∫
∫◻
|◻|
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

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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 (5)

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