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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x/(3x²-1)^4
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Integral of x*sin(x)^2
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Integral of dx/(5-12*x-9*x^2)
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Integral of 4/x^2
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Identical expressions
- xsin(x)/(one +cos(x))⁴
- x sinus of (x) divide by (1 plus co sinus of e of (x))⁴
- x sinus of (x) divide by (one plus co sinus of e of (x))⁴
- xsinx/1+cosx⁴
- xsin(x) divide by (1+cos(x))⁴
- xsin(x)/(1+cos(x))⁴dx
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Similar expressions
- xsin(x)/(1-cos(x))⁴
- xsinx/(1+cosx)⁴
Integral of xsin(x)/(1+cos(x))⁴ dx
The solution
You have entered
[src]
pi -- 2 / | | x*sin(x) | ------------- dx | 4 | (1 + cos(x)) | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} \frac{x \sin{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{4}}\, dx$$
Integral((x*sin(x))/(1 + cos(x))^4, (x, 0, pi/2))
The answer (Indefinite)
[src]
/ /x\ 3/x\ 5/x\ 2/x\ 4/x\ 6/x\ | tan|-| tan |-| tan |-| x*tan |-| x*tan |-| x*tan |-| | x*sin(x) \2/ \2/ \2/ x \2/ \2/ \2/ | ------------- dx = C - ------ - ------- - ------- + -- + --------- + --------- + --------- | 4 12 18 60 24 8 8 24 | (1 + cos(x)) | /
$$\int \frac{x \sin{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{4}}\, dx = C + \frac{x \tan^{6}{\left(\frac{x}{2} \right)}}{24} + \frac{x \tan^{4}{\left(\frac{x}{2} \right)}}{8} + \frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{8} + \frac{x}{24} - \frac{\tan^{5}{\left(\frac{x}{2} \right)}}{60} - \frac{\tan^{3}{\left(\frac{x}{2} \right)}}{18} - \frac{\tan{\left(\frac{x}{2} \right)}}{12}$$
The graph
The answer
[src]
7 pi - -- + -- 45 6
$$- \frac{7}{45} + \frac{\pi}{6}$$
=
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7 pi - -- + -- 45 6
$$- \frac{7}{45} + \frac{\pi}{6}$$
-7/45 + pi/6
Use the examples entering the upper and lower limits of integration.