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How to use it?
- Integral of d{x}:
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Integral of 1/5x
- Integral of sqrt(1+e^(2x))
- Integral of sinx/cos2x
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Integral of sqrt(1-x^2)dx
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Identical expressions
- one /(sin(x+y^ two))
- 1 divide by ( sinus of (x plus y squared ))
- one divide by ( sinus of (x plus y to the power of two))
- 1/(sin(x+y2))
- 1/sinx+y2
- 1/(sin(x+y²))
- 1/(sin(x+y to the power of 2))
- 1/sinx+y^2
- 1 divide by (sin(x+y^2))
- 1/(sin(x+y^2))dx
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Similar expressions
- 1/(sin(x-y^2))
Integral of 1/(sin(x+y^2)) dx
The solution
You have entered
[src]
1 / | | 1 | ----------- dx | / 2\ | sin\x + y / | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin{\left(x + y^{2} \right)}}\, dx$$
Integral(1/sin(x + y^2), (x, 0, 1))
The answer (Indefinite)
[src]
/ | / / 2\\ | 1 | |x y || | ----------- dx = C + log|tan|- + --|| | / 2\ \ \2 2 // | sin\x + y / | /
$$\int \frac{1}{\sin{\left(x + y^{2} \right)}}\, dx = C + \log{\left(\tan{\left(\frac{x}{2} + \frac{y^{2}}{2} \right)} \right)}$$
The answer
[src]
/ / 2\\ / / 2\\
| |y || | |1 y ||
- log|tan|--|| + log|tan|- + --||
\ \2 // \ \2 2 //
$$- \log{\left(\tan{\left(\frac{y^{2}}{2} \right)} \right)} + \log{\left(\tan{\left(\frac{y^{2}}{2} + \frac{1}{2} \right)} \right)}$$
=
=
/ / 2\\ / / 2\\
| |y || | |1 y ||
- log|tan|--|| + log|tan|- + --||
\ \2 // \ \2 2 //
$$- \log{\left(\tan{\left(\frac{y^{2}}{2} \right)} \right)} + \log{\left(\tan{\left(\frac{y^{2}}{2} + \frac{1}{2} \right)} \right)}$$
-log(tan(y^2/2)) + log(tan(1/2 + y^2/2))
Use the examples entering the upper and lower limits of integration.