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Solve the trigonometric integral $\int\mathrm{arcsec}\left(\frac{1}{x}\right)dx$

Used Formulas

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Solution

Formulas

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Derivatives of inverse trigonometric functions

$\frac{d}{dx}\left(\mathrm{arcsec}\left(\theta \right)\right)=\frac{1}{\theta \sqrt{\theta ^2-1}}\frac{d}{dx}\left(\theta \right)$

Basic Derivatives

· Quotient Rule in Differentiation
$\frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}$
· Derivative of a Constant
$\frac{d}{dx}\left(c\right)=0$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Basic Integrals

· Integral of a Constant
$\int cdx=cvar+C$

Integration Techniques

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

Trigonometric Integrals

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

Function Plot

Plotting: $x\mathrm{arcsec}\left(\frac{1}{x}\right)-\sqrt{1-x^2}+C_0$

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0
a
b
c
d
f
g
m
n
u
v
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x
y
z
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(◻)
+
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×
◻/◻
/
÷
◻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: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

Used Formulas

See formulas (7)

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