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Solve the trigonometric integral $\int7\csc\left(x\right)^3dx$

Step-by-step Solution

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Solution

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Final answer to the problem

$-\frac{7}{8}\cot\left(x\right)\csc\left(x\right)-\frac{7}{8}\ln\left|\csc\left(x\right)+\cot\left(x\right)\right|+C_0$
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Step-by-step Solution

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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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The integral of a function times a constant ($7$) is equal to the constant times the integral of the function

$7\int\csc\left(x\right)^3dx$

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

$7\int\csc\left(x\right)^3dx$

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Learn how to solve definite integrals problems step by step online. Solve the trigonometric integral int(7csc(x)^3)dx. The integral of a function times a constant (7) is equal to the constant times the integral of the function. Rewrite the trigonometric function \csc\left(x\right)^3 as the product of two lower exponents. We can solve the integral \int\csc\left(x\right)^2\csc\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du.

Final answer to the problem

$-\frac{7}{8}\cot\left(x\right)\csc\left(x\right)-\frac{7}{8}\ln\left|\csc\left(x\right)+\cot\left(x\right)\right|+C_0$

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Function Plot

Plotting: $-\frac{7}{8}\cot\left(x\right)\csc\left(x\right)-\frac{7}{8}\ln\left(\csc\left(x\right)+\cot\left(x\right)\right)+C_0$

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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
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: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Used Formulas

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