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Solve the trigonometric integral $\int\frac{1}{4-5\sin\left(x\right)}dx$

Step-by-step Solution

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Final answer to the problem

$\frac{1}{3}\ln\left|\tan\left(\frac{x}{2}\right)-2\right|-\frac{1}{3}\ln\left|2\tan\left(\frac{x}{2}\right)-1\right|+C_0$
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Step-by-step Solution

How should I solve this problem?

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  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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We can solve the integral $\int\frac{1}{4-5\sin\left(x\right)}dx$ by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of $t$ by setting the substitution

$t=\tan\left(\frac{x}{2}\right)$

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

$t=\tan\left(\frac{x}{2}\right)$

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Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(1/(4-5sin(x)))dx. We can solve the integral \int\frac{1}{4-5\sin\left(x\right)}dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get. Simplifying.

Final answer to the problem

$\frac{1}{3}\ln\left|\tan\left(\frac{x}{2}\right)-2\right|-\frac{1}{3}\ln\left|2\tan\left(\frac{x}{2}\right)-1\right|+C_0$

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Function Plot

Plotting: $\frac{1}{3}\ln\left|\tan\left(\frac{x}{2}\right)-2\right|-\frac{1}{3}\ln\left|2\tan\left(\frac{x}{2}\right)-1\right|+C_0$

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7
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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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