Sr Examen
Integral de cos^2(x)/(3+sinx) dx
Solución
Ha introducido
[src]
1 / | | 2 | cos (x) | ---------- dx | 3 + sin(x) | / 0
$$\int\limits_{0}^{1} \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} + 3}\, dx$$
Integral(cos(x)^2/(3 + sin(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / ___ /x\\\ / /x pi\ / ___ /x\\\ / | |- - --| | ___ 3*\/ 2 *tan|-||| | |- - --| | ___ 3*\/ 2 *tan|-||| | ___ | |2 2 | |\/ 2 \2/|| 2/x\ ___ 2/x\ | |2 2 | |\/ 2 \2/|| | 2 4*\/ 2 *|pi*floor|------| + atan|----- + --------------|| 3*x*tan |-| 4*\/ 2 *tan |-|*|pi*floor|------| + atan|----- + --------------|| | cos (x) 2 3*x \ \ pi / \ 4 4 // \2/ \2/ \ \ pi / \ 4 4 // | ---------- dx = C + ----------- + ----------- - --------------------------------------------------------- + ----------- - ----------------------------------------------------------------- | 3 + sin(x) 2/x\ 2/x\ 2/x\ 2/x\ 2/x\ | 1 + tan |-| 1 + tan |-| 1 + tan |-| 1 + tan |-| 1 + tan |-| / \2/ \2/ \2/ \2/ \2/
$$\int \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)} + 3}\, dx = C + \frac{3 x \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{3 x}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(\operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(\frac{x}{2} \right)}}{4} + \frac{\sqrt{2}}{4} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(\operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(\frac{x}{2} \right)}}{4} + \frac{\sqrt{2}}{4} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{2}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}$$
Gráfica
Respuesta
[src]
/ / ___ ___ \\ / / ___ ___ \\
___ | |\/ 2 3*\/ 2 *tan(1/2)|| ___ 2 | |\/ 2 3*\/ 2 *tan(1/2)||
2 / / ___\\ 4*\/ 2 *|-pi + atan|----- + ----------------|| 4*\/ 2 *tan (1/2)*|-pi + atan|----- + ----------------||
5 3*tan (1/2) ___ | |\/ 2 || \ \ 4 4 // \ \ 4 4 //
-2 + ------------- + ------------- + 4*\/ 2 *|-pi + atan|-----|| - ---------------------------------------------- - --------------------------------------------------------
2 2 \ \ 4 // 2 2
1 + tan (1/2) 1 + tan (1/2) 1 + tan (1/2) 1 + tan (1/2)
$$4 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right) - 2 + \frac{3 \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2} \tan{\left(\frac{1}{2} \right)}}{4} \right)}\right) \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} + \frac{5}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2} \tan{\left(\frac{1}{2} \right)}}{4} \right)}\right)}{\tan^{2}{\left(\frac{1}{2} \right)} + 1}$$
=
=
/ / ___ ___ \\ / / ___ ___ \\
___ | |\/ 2 3*\/ 2 *tan(1/2)|| ___ 2 | |\/ 2 3*\/ 2 *tan(1/2)||
2 / / ___\\ 4*\/ 2 *|-pi + atan|----- + ----------------|| 4*\/ 2 *tan (1/2)*|-pi + atan|----- + ----------------||
5 3*tan (1/2) ___ | |\/ 2 || \ \ 4 4 // \ \ 4 4 //
-2 + ------------- + ------------- + 4*\/ 2 *|-pi + atan|-----|| - ---------------------------------------------- - --------------------------------------------------------
2 2 \ \ 4 // 2 2
1 + tan (1/2) 1 + tan (1/2) 1 + tan (1/2) 1 + tan (1/2)
$$4 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right) - 2 + \frac{3 \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2} \tan{\left(\frac{1}{2} \right)}}{4} \right)}\right) \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} + \frac{5}{\tan^{2}{\left(\frac{1}{2} \right)} + 1} - \frac{4 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} + \frac{3 \sqrt{2} \tan{\left(\frac{1}{2} \right)}}{4} \right)}\right)}{\tan^{2}{\left(\frac{1}{2} \right)} + 1}$$
-2 + 5/(1 + tan(1/2)^2) + 3*tan(1/2)^2/(1 + tan(1/2)^2) + 4*sqrt(2)*(-pi + atan(sqrt(2)/4)) - 4*sqrt(2)*(-pi + atan(sqrt(2)/4 + 3*sqrt(2)*tan(1/2)/4))/(1 + tan(1/2)^2) - 4*sqrt(2)*tan(1/2)^2*(-pi + atan(sqrt(2)/4 + 3*sqrt(2)*tan(1/2)/4))/(1 + tan(1/2)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.