Try NerdPal! Our new app on iOS and Android

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

## Step-by-step Solution

Go!
Go!
1
2
3
4
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

### Videos

$-\ln\left(\cos\left(x\right)\right)+x+C_0$
Got another answer? Verify it here!

## Step-by-step Solution

Problem to solve:

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

Specify the solving method

1

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. 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).

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

### Explore different ways to solve this problem

Basic IntegralsIntegration by SubstitutionIntegration by PartsWeierstrass Substitution
SnapXam A2

### beta Got another answer? Verify it!

Go!
1
2
3
4
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

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

### Main topic:

Trigonometric Integrals

~ 0.09 s