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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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Solution

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Final Answer

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

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

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Unlock the first 2 steps of this solution.

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.

Final Answer

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

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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a
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(◻)
+
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◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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:

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Main topic:

Trigonometric Integrals

Used formulas:

1. See formulas

Time to solve it:

~ 0.03 s

Related topics:

Trigonometric IntegralsIntegral CalculusCalculusIntegration Techniques

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