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Find the integral $\int x^4\sin\left(x\right)dx$

Used Formulas

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ln
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asin
acos
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acot
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sinh
cosh
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coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Basic Derivatives

· Power rule for derivatives
$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$
· Derivative of a Constant
$\frac{d}{dx}\left(c\right)=0$

Trigonometric Integrals

· Integral of the sine function
$\int\sin\left(\theta \right)dx=-\cos\left(\theta \right)+C$
· Integral of the cosine function
$\int\cos\left(\theta \right)dx=\sin\left(\theta \right)+C$

Basic Integrals

· Constant factor Rule
$\int cxdx=c\int xdx$

Function Plot

Plotting: $-x^4\cos\left(x\right)+4x^{3}\sin\left(x\right)+12x^{2}\cos\left(x\right)-24x\sin\left(x\right)-24\cos\left(x\right)+C_0$

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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
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: 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.

Used Formulas

See formulas (7)

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