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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(x(1-x))
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Integral of sin^3(x)/cos^2(x)
- Integral of ln(x+(1+x^2)^(1/2))
- Integral of e^x^2(ln2^(x/2))
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Identical expressions
- one /(one +(cos(x))^ two)
- 1 divide by (1 plus ( co sinus of e of (x)) squared )
- one divide by (one plus ( co sinus of e of (x)) to the power of two)
- 1/(1+(cos(x))2)
- 1/1+cosx2
- 1/(1+(cos(x))²)
- 1/(1+(cos(x)) to the power of 2)
- 1/1+cosx^2
- 1 divide by (1+(cos(x))^2)
- 1/(1+(cos(x))^2)dx
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Similar expressions
- 1/(1-(cos(x))^2)
- 1/(1+(cosx)^2)
Integral of 1/(1+(cos(x))^2) dx
The solution
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[src]
pi / | | 1 | ----------- dx | 2 | 1 + cos (x) | / 0
$$\int\limits_{0}^{\pi} \frac{1}{\cos^{2}{\left(x \right)} + 1}\, dx$$
Integral(1/(1 + cos(x)^2), (x, 0, pi))
The answer (Indefinite)
[src]
/ /x pi\ \ / /x pi\ \
| |- - --| | | |- - --| |
/ ___ | |2 2 | / ___ /x\\| ___ | |2 2 | / ___ /x\\|
| \/ 2 *|pi*floor|------| + atan|1 + \/ 2 *tan|-||| \/ 2 *|pi*floor|------| + atan|-1 + \/ 2 *tan|-|||
| 1 \ \ pi / \ \2/// \ \ pi / \ \2///
| ----------- dx = C + ------------------------------------------------- + --------------------------------------------------
| 2 2 2
| 1 + cos (x)
|
/
$$\int \frac{1}{\cos^{2}{\left(x \right)} + 1}\, dx = C + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{x}{2} \right)} - 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2} + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{x}{2} \right)} + 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2}$$
The graph
The answer
[src]
___ pi*\/ 2 -------- 2
$$\frac{\sqrt{2} \pi}{2}$$
=
=
___ pi*\/ 2 -------- 2
$$\frac{\sqrt{2} \pi}{2}$$
pi*sqrt(2)/2
Use the examples entering the upper and lower limits of integration.