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Algebra Baldor
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Solve the trigonometric integral $\int\sec\left(\pi x\right)^3dx$

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 Integrals

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

Derivatives of trigonometric functions

· Derivative of secant function
$\frac{d}{dx}\left(\sec\left(\theta \right)\right)=\frac{d}{dx}\left(\theta \right)\sec\left(\theta \right)\tan\left(\theta \right)$

Basic Derivatives

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

Trigonometric Integrals

$\int\sec\left(\theta \right)^2dx=\tan\left(\theta \right)+C$
$\int\sec\left(\theta \right)\tan\left(\theta \right)^2dx=\int\sec\left(\theta \right)^3dx-\int\sec\left(\theta \right)dx$
$\int\sec\left(\theta \right)dx=\ln\left(\sec\left(\theta \right)+\tan\left(\theta \right)\right)+C$

Function Plot

Plotting: $\frac{invfrac\left(\pi \right)\tan\left(\pi x\right)\sec\left(\pi x\right)+invfrac\left(\pi \right)\ln\left(\sec\left(\pi x\right)+\tan\left(\pi x\right)\right)}{invfrac\left(\pi \right)+1}+C_0$

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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: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

Used Formulas

See formulas (8)

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