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Find the integral $\int\frac{-\sin\left(nx\right)}{n^2}dx$

Step-by-step Solution

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Final answer to the problem

$\frac{\cos\left(nx\right)}{n^{3}}+C_0$
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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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1

Take out the constant $-1$ from the integral

$-\int\frac{\sin\left(nx\right)}{n^2}dx$

Learn how to solve integral calculus problems step by step online.

$-\int\frac{\sin\left(nx\right)}{n^2}dx$

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Learn how to solve integral calculus problems step by step online. Find the integral int((-sin(nx))/(n^2))dx. Take out the constant -1 from the integral. Take the constant \frac{1}{n^2} out of the integral. Multiplying the fraction by -1. We can solve the integral \int\sin\left(nx\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that nx it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.

Final answer to the problem

$\frac{\cos\left(nx\right)}{n^{3}}+C_0$

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Function Plot

Plotting: $\frac{\cos\left(nx\right)}{n^{3}}+C_0$

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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

How to improve your answer:

Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Used Formulas

See formulas (2)

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