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Solve the trigonometric integral $\int\frac{1}{2\sin\left(x\right)\cos\left(x\right)}dx$

Used Formulas

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Solution

Formulas

Videos

Basic Integrals

· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$

Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$

Function Plot

Plotting: $-\frac{1}{2}\ln\left(1-\tan\left(\frac{x}{2}\right)^{2}\right)+\frac{1}{2}\ln\left(\tan\left(\frac{x}{2}\right)\right)+C_0$

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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
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: Weierstrass Substitution

In integral calculus, the Weierstrass substitution or tangent half angle substitution is a method for solving integrals, which converts a rational expression of trigonometric functions into an algebraic rational function, which can be easier to integrate. The Weierstrass substitution is very useful for integrals that involve a simple rational expression with sine and/or cosine in the denominator.

Used Formulas

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