Mister Exam
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- Improper integral
- Double Integral
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- Curvilinear integral
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How to use it?
- Integral of d{x}:
- Integral of (sin(2021)x)/(pi*sin(x))
- Integral of e^(x)*cos(y)
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Integral of sin(4x)cos(4x)dx
- Integral of sqrt(x^3-2x^2+x)
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Identical expressions
- (sin(two thousand and twenty-one)x)/(pi*sin(x))
- ( sinus of (2021)x) divide by ( Pi multiply by sinus of (x))
- ( sinus of (two thousand and twenty minus one)x) divide by ( Pi multiply by sinus of (x))
- (sin(2021)x)/(pisin(x))
- sin2021x/pisinx
- (sin(2021)x) divide by (pi*sin(x))
- (sin(2021)x)/(pi*sin(x))dx
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Similar expressions
- (sin2021x)/(pisinx)
- (sin2021x)/(pi*sinx)
- sin(2021x)/(pi*sin(x))
- sin(2021x)/(pi*sinx)
- (sin(2021)x)/(pi*sinx)
Integral of (sin(2021)x)/(pi*sin(x)) dx
The solution
You have entered
[src]
pi / | | sin(2021)*x | ----------- dx | pi*sin(x) | / 0
$$\int\limits_{0}^{\pi} \frac{x \sin{\left(2021 \right)}}{\pi \sin{\left(x \right)}}\, dx$$
Integral(sin(2021)*x/((pi*sin(x))), (x, 0, pi))
Detail solution
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The integral of a constant times a function is the constant times the integral of the function:
-
Don't know the steps in finding this integral.
But the integral is
So, the result is:
-
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/
|
| x
| ------ dx*sin(2021)
/ | sin(x)
| |
| sin(2021)*x /
| ----------- dx = C + ----------------------
| pi*sin(x) pi
|
/
$$-{{\sin 2021\,\left(x\,\log \left(\sin ^2x+\cos ^2x+2\,\cos x+1
\right)-x\,\log \left(\sin ^2x+\cos ^2x-2\,\cos x+1\right)+2\,i\,x\,
{\rm atan2}\left(\sin x , \cos x+1\right)+2\,i\,x\,{\rm atan2}\left(
\sin x , 1-\cos x\right)+2\,i\,{\it li}_{2}(e^{i\,x})-2\,i\,{\it li}
_{2}(-e^{i\,x})\right)}\over{2\,\pi}}$$
The answer
[src]
pi
/
|
| x
| ------ dx*sin(2021)
| sin(x)
|
/
0
-----------------------
pi
$$\frac{\sin{\left(2021 \right)} \int\limits_{0}^{\pi} \frac{x}{\sin{\left(x \right)}}\, dx}{\pi}$$
=
=
pi
/
|
| x
| ------ dx*sin(2021)
| sin(x)
|
/
0
-----------------------
pi
$$\frac{\sin{\left(2021 \right)} \int\limits_{0}^{\pi} \frac{x}{\sin{\left(x \right)}}\, dx}{\pi}$$
Use the examples entering the upper and lower limits of integration.