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

## Step-by-step Solution

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###  Videos

$-\ln\left(\cos\left(x\right)\right)+C_0$
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##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

1

Simplify $\frac{\sin\left(x\right)}{\cos\left(x\right)}$ into $\tan\left(x\right)$ by applying trigonometric identities

$\int\tan\left(x\right)dx$

Learn how to solve trigonometric integrals problems step by step online.

$\int\tan\left(x\right)dx$

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int((sin(x)/(cos(x))dx. Simplify \frac{\sin\left(x\right)}{\cos\left(x\right)} into \tan\left(x\right) by applying trigonometric identities. The integral of the tangent function is given by the following formula, \displaystyle\int\tan(x)dx=-\ln(\cos(x)). As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

$-\ln\left(\cos\left(x\right)\right)+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int((sin(x)/(cos(x))dx using basic integralsSolve int((sin(x)/(cos(x))dx using u-substitutionSolve int((sin(x)/(cos(x))dx using integration by partsSolve int((sin(x)/(cos(x))dx using weierstrass substitution

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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
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:

Trigonometric Integrals

~ 0.03 s

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