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# Find the integral $\int x\arctan\left(4x\right)dx$

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asin
acos
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sinh
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asinh
acosh
atanh
acoth
asech
acsch

## Derivatives of inverse trigonometric functions

$\frac{d}{dx}\left(\arctan\left(\theta \right)\right)=\frac{1}{1+\theta ^2}\frac{d}{dx}\left(\theta \right)$

## Basic Derivatives

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

## Basic Integrals

· Power Rule of Integration
$\int xdx=\frac{1}{2}x^2+C$
· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$
· Integral of a Constant
$\int cdx=cvar+C$

## Integration Techniques

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

## Integrals of Rational Functions

$\int\frac{n}{a+b}dx=n\int\frac{1}{a+b}dx$

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: 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.