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

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##  Final Answer

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

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Expand the fraction $\frac{\sin\left(x\right)+\cos\left(x\right)}{\cos\left(x\right)}$ into $2$ simpler fractions with common denominator $\cos\left(x\right)$

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

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

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

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int((sin(x)+cos(x))/cos(x))dx. Expand the fraction \frac{\sin\left(x\right)+\cos\left(x\right)}{\cos\left(x\right)} into 2 simpler fractions with common denominator \cos\left(x\right). Simplify the resulting fractions. Expand the integral \int\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}+1\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{\sin\left(x\right)}{\cos\left(x\right)}dx results in: -\ln\left(\cos\left(x\right)\right).

##  Final Answer

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

##  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

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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

Integrals that contain trigonometric functions and their powers.

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