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

## Step-by-step Solution

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###  Formulas

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

Problem to solve:

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

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The integral $\int\frac{\sin\left(x\right)}{\cos\left(x\right)}dx$ results in: $-\ln\left(\cos\left(x\right)\right)$

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

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

Learn how to solve problems step by step online. Solve the trigonometric integral int((sin(x)+cos(x))/(cos(x))dx. The integral \int\frac{\sin\left(x\right)}{\cos\left(x\right)}dx results in: -\ln\left(\cos\left(x\right)\right). The integral \int1dx results in: x. Gather the results of all integrals. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

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

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

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5
6
7
8
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
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

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