Mister Exam
Other calculators
- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Integral of d{x}:
-
Integral of cotx
- Integral of xlnxdx
-
Integral of tan⁵x
-
Integral of ln2x
-
Identical expressions
- one /(one +sin^ two (x)/ six)
- 1 divide by (1 plus sinus of squared (x) divide by 6)
- one divide by (one plus sinus of to the power of two (x) divide by six)
- 1/(1+sin2(x)/6)
- 1/1+sin2x/6
- 1/(1+sin²(x)/6)
- 1/(1+sin to the power of 2(x)/6)
- 1/1+sin^2x/6
- 1 divide by (1+sin^2(x) divide by 6)
- 1/(1+sin^2(x)/6)dx
-
Similar expressions
- 1/(1-sin^2(x)/6)
Integral of 1/(1+sin^2(x)/6) dx
The solution
You have entered
[src]
pi -- 4 / | | 1 | ----------- dx | 2 | sin (x) | 1 + ------- | 6 | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \frac{1}{\frac{\sin^{2}{\left(x \right)}}{6} + 1}\, dx$$
Integral(1/(1 + sin(x)^2/6), (x, 0, pi/4))
The answer (Indefinite)
[src]
/ /x pi\ / ___ /x\ \\ / /x pi\ / ___ /x\ \\ / /x pi\ / ___ /x\ \\ / /x pi\ / ___ /x\ \\
| |- - --| | \/ 3 *tan|-| || | |- - --| | \/ 3 *tan|-| || ___________ ___________ | |- - --| | \/ 3 *tan|-| || ___________ ___________ | |- - --| | \/ 3 *tan|-| ||
____ | |2 2 | | \2/ || ___ | |2 2 | | \2/ || ____ / ___ / ___ | |2 2 | | \2/ || ___ / ___ / ___ | |2 2 | | \2/ ||
18*\/ 21 *|pi*floor|------| + atan|--------------|| 72*\/ 3 *|pi*floor|------| + atan|--------------|| 6*\/ 21 *\/ 4 + \/ 7 *\/ 4 - \/ 7 *|pi*floor|------| + atan|--------------|| 24*\/ 3 *\/ 4 + \/ 7 *\/ 4 - \/ 7 *|pi*floor|------| + atan|--------------||
/ | \ pi / | ___________|| | \ pi / | ___________|| | \ pi / | ___________|| | \ pi / | ___________||
| | | / ___ || | | / ___ || | | / ___ || | | / ___ ||
| 1 \ \\/ 4 - \/ 7 // \ \\/ 4 - \/ 7 // \ \\/ 4 + \/ 7 // \ \\/ 4 + \/ 7 //
| ----------- dx = C + --------------------------------------------------- + -------------------------------------------------- + -------------------------------------------------------------------------------- + --------------------------------------------------------------------------------
| 2 ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________
| sin (x) / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___
| 1 + ------- 105*\/ 4 - \/ 7 + 33*\/ 7 *\/ 4 - \/ 7 105*\/ 4 - \/ 7 + 33*\/ 7 *\/ 4 - \/ 7 105*\/ 4 - \/ 7 + 33*\/ 7 *\/ 4 - \/ 7 105*\/ 4 - \/ 7 + 33*\/ 7 *\/ 4 - \/ 7
| 6
|
/
$$\int \frac{1}{\frac{\sin^{2}{\left(x \right)}}{6} + 1}\, dx = C + \frac{18 \sqrt{21} \left(\operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{x}{2} \right)}}{\sqrt{4 - \sqrt{7}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{33 \sqrt{7} \sqrt{4 - \sqrt{7}} + 105 \sqrt{4 - \sqrt{7}}} + \frac{72 \sqrt{3} \left(\operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{x}{2} \right)}}{\sqrt{4 - \sqrt{7}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{33 \sqrt{7} \sqrt{4 - \sqrt{7}} + 105 \sqrt{4 - \sqrt{7}}} + \frac{6 \sqrt{21} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \left(\operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{x}{2} \right)}}{\sqrt{\sqrt{7} + 4}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{33 \sqrt{7} \sqrt{4 - \sqrt{7}} + 105 \sqrt{4 - \sqrt{7}}} + \frac{24 \sqrt{3} \sqrt{4 - \sqrt{7}} \sqrt{\sqrt{7} + 4} \left(\operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{x}{2} \right)}}{\sqrt{\sqrt{7} + 4}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{33 \sqrt{7} \sqrt{4 - \sqrt{7}} + 105 \sqrt{4 - \sqrt{7}}}$$
The graph
Use the examples entering the upper and lower limits of integration.