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

Step-by-step Solution

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ln
log
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sin
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asin
acos
atan
acot
asec
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final answer to the problem

$\ln\left|\sec\left(x\right)+\tan\left(x\right)\right|+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Integrate using tabular integration
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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Rewrite the trigonometric expression $\frac{1}{\cos\left(x\right)}$ inside the integral

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

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

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

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Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(1/cos(x))dx. Rewrite the trigonometric expression \frac{1}{\cos\left(x\right)} inside the integral. The integral of the secant function is given by the following formula, \displaystyle\int\sec(x)dx=\ln\left|\sec(x)+\tan(x)\right|. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

Final answer to the problem

$\ln\left|\sec\left(x\right)+\tan\left(x\right)\right|+C_0$

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Function Plot

Plotting: $\ln\left(\sec\left(x\right)+\tan\left(x\right)\right)+C_0$

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1
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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

How to improve your answer:

Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

Used Formulas

See formulas (1)

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