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Solve the trigonometric integral $\int\sin\left(nx\right)dx$

Step-by-step Solution

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sin
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asin
acos
atan
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sinh
cosh
tanh
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asinh
acosh
atanh
acoth
asech
acsch

Final Answer

$\frac{-2}{\sec\left(\frac{x}{2}\right)^2}+C_0$
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Step-by-step Solution

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We can solve the integral $\int\sin\left(nx\right)dx$ 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

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

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

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Learn how to solve integral calculus problems step by step online. Solve the trigonometric integral int(sin(nx))dx. We can solve the integral \int\sin\left(nx\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

$\frac{-2}{\sec\left(\frac{x}{2}\right)^2}+C_0$

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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

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Function Plot

Plotting: $\frac{-2}{\sec\left(\frac{x}{2}\right)^2}+C_0$

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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

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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.

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