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Find the integral $\int2x\sin\left(2x\right)dx$

Used Formulas

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Solution

Formulas

Videos

Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$
· Integration by Parts
$\int udv=uv - \int vdu$

Basic Derivatives

· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

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: $-x\cos\left(2x\right)+\frac{1}{2}\sin\left(2x\right)+C_0$

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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
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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$\int\:x^2\:sen\:3x\:dx$

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 (6)

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