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Solve the trigonometric integral $\int\sec\left(2x\right)^3dx$

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
$\int udv=uv - \int vdu$

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: $\tan\left(2x\right)\sec\left(2x\right)+\ln\left(\sec\left(2x\right)+\tan\left(2x\right)\right)+C_0$

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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
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

How to improve your answer:

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Find the integral

$\int\frac{dx}{1-sin\left(x\right)}$

Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

Used Formulas

See formulas (5)

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