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- Improper integral
- Double Integral
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How to use it?
- Integral of d{x}:
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Integral of x√(x+1)
- Integral of sin^-1(x)
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Integral of x(x^2+1)^3
- Integral of e^(1/x)
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Identical expressions
- (one +sin(x))* one /(one -sin(x))^ two
- (1 plus sinus of (x)) multiply by 1 divide by (1 minus sinus of (x)) squared
- (one plus sinus of (x)) multiply by one divide by (one minus sinus of (x)) to the power of two
- (1+sin(x))*1/(1-sin(x))2
- 1+sinx*1/1-sinx2
- (1+sin(x))*1/(1-sin(x))²
- (1+sin(x))*1/(1-sin(x)) to the power of 2
- (1+sin(x))1/(1-sin(x))^2
- (1+sin(x))1/(1-sin(x))2
- 1+sinx1/1-sinx2
- 1+sinx1/1-sinx^2
- (1+sin(x))*1 divide by (1-sin(x))^2
- (1+sin(x))*1/(1-sin(x))^2dx
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Similar expressions
- (1-sin(x))*1/(1-sin(x))^2
- (1+sin(x))*1/(1+sin(x))^2
- (1+sinx)*1/(1-sinx)^2
Integral of (1+sin(x))*1/(1-sin(x))^2 dx
The solution
You have entered
[src]
pi -- 4 / | | 1 + sin(x) | ------------- dx | 2 | (1 - sin(x)) | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \frac{\sin{\left(x \right)} + 1}{\left(1 - \sin{\left(x \right)}\right)^{2}}\, dx$$
Integral((1 + sin(x))/(1 - sin(x))^2, (x, 0, pi/4))
The answer (Indefinite)
[src]
/ 2/x\ | 6*tan |-| | 1 + sin(x) 2 \2/ | ------------- dx = C - ------------------------------------- - ------------------------------------- | 2 2/x\ 3/x\ /x\ 2/x\ 3/x\ /x\ | (1 - sin(x)) -3 - 9*tan |-| + 3*tan |-| + 9*tan|-| -3 - 9*tan |-| + 3*tan |-| + 9*tan|-| | \2/ \2/ \2/ \2/ \2/ \2/ /
$$\int \frac{\sin{\left(x \right)} + 1}{\left(1 - \sin{\left(x \right)}\right)^{2}}\, dx = C - \frac{6 \tan^{2}{\left(\frac{x}{2} \right)}}{3 \tan^{3}{\left(\frac{x}{2} \right)} - 9 \tan^{2}{\left(\frac{x}{2} \right)} + 9 \tan{\left(\frac{x}{2} \right)} - 3} - \frac{2}{3 \tan^{3}{\left(\frac{x}{2} \right)} - 9 \tan^{2}{\left(\frac{x}{2} \right)} + 9 \tan{\left(\frac{x}{2} \right)} - 3}$$
The graph
The answer
[src]
2
/ ___\
2 2 6*\-1 + \/ 2 /
- - - ------------------------------------------------- - -------------------------------------------------
3 2 3 2 3
/ ___\ / ___\ ___ / ___\ / ___\ ___
-12 - 9*\-1 + \/ 2 / + 3*\-1 + \/ 2 / + 9*\/ 2 -12 - 9*\-1 + \/ 2 / + 3*\-1 + \/ 2 / + 9*\/ 2
$$- \frac{2}{3} - \frac{6 \left(-1 + \sqrt{2}\right)^{2}}{-12 - 9 \left(-1 + \sqrt{2}\right)^{2} + 3 \left(-1 + \sqrt{2}\right)^{3} + 9 \sqrt{2}} - \frac{2}{-12 - 9 \left(-1 + \sqrt{2}\right)^{2} + 3 \left(-1 + \sqrt{2}\right)^{3} + 9 \sqrt{2}}$$
=
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2
/ ___\
2 2 6*\-1 + \/ 2 /
- - - ------------------------------------------------- - -------------------------------------------------
3 2 3 2 3
/ ___\ / ___\ ___ / ___\ / ___\ ___
-12 - 9*\-1 + \/ 2 / + 3*\-1 + \/ 2 / + 9*\/ 2 -12 - 9*\-1 + \/ 2 / + 3*\-1 + \/ 2 / + 9*\/ 2
$$- \frac{2}{3} - \frac{6 \left(-1 + \sqrt{2}\right)^{2}}{-12 - 9 \left(-1 + \sqrt{2}\right)^{2} + 3 \left(-1 + \sqrt{2}\right)^{3} + 9 \sqrt{2}} - \frac{2}{-12 - 9 \left(-1 + \sqrt{2}\right)^{2} + 3 \left(-1 + \sqrt{2}\right)^{3} + 9 \sqrt{2}}$$
-2/3 - 2/(-12 - 9*(-1 + sqrt(2))^2 + 3*(-1 + sqrt(2))^3 + 9*sqrt(2)) - 6*(-1 + sqrt(2))^2/(-12 - 9*(-1 + sqrt(2))^2 + 3*(-1 + sqrt(2))^3 + 9*sqrt(2))
Use the examples entering the upper and lower limits of integration.