Sr Examen
Integral de sqrt(1-x*x)/((x*x*x*x*x*x)) dx
Solución
Ha introducido
[src]
1 / | | _________ | \/ 1 - x*x | ----------- dx | x*x*x*x*x*x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{- x x + 1}}{x x x x x x}\, dx$$
Integral(sqrt(1 - x*x)/((((((x*x)*x)*x)*x)*x)), (x, 0, 1))
Gráfica
Respuesta
[src]
1 / | | / _________ _________ _________ | | / 2 / 2 / 2 | | 2*I I*\/ -1 + x 2*I*\/ -1 + x I*\/ -1 + x I I 2 | |--------------- + -------------- - ---------------- - -------------- - ----------------- + ------------------ for x > 1 | | _________ 6 2 4 _________ _________ | | / 2 x 15*x 5*x 4 / 2 2 / 2 | |15*\/ -1 + x 5*x *\/ -1 + x 15*x *\/ -1 + x | < dx | | ________ ________ ________ | | / 2 / 2 / 2 | | 2 \/ 1 - x 2*\/ 1 - x \/ 1 - x 1 1 | | - -------------- + ----------- - ------------- - ----------- - ----------------- + ---------------- otherwise | | ________ 6 2 4 ________ ________ | | / 2 x 15*x 5*x 2 / 2 4 / 2 | \ 15*\/ 1 - x 15*x *\/ 1 - x 5*x *\/ 1 - x | / 0
$$\int\limits_{0}^{1} \begin{cases} \frac{2 i}{15 \sqrt{x^{2} - 1}} - \frac{2 i \sqrt{x^{2} - 1}}{15 x^{2}} + \frac{i}{15 x^{2} \sqrt{x^{2} - 1}} - \frac{i \sqrt{x^{2} - 1}}{5 x^{4}} - \frac{i}{5 x^{4} \sqrt{x^{2} - 1}} + \frac{i \sqrt{x^{2} - 1}}{x^{6}} & \text{for}\: x^{2} > 1 \\- \frac{2}{15 \sqrt{1 - x^{2}}} - \frac{2 \sqrt{1 - x^{2}}}{15 x^{2}} - \frac{1}{15 x^{2} \sqrt{1 - x^{2}}} - \frac{\sqrt{1 - x^{2}}}{5 x^{4}} + \frac{1}{5 x^{4} \sqrt{1 - x^{2}}} + \frac{\sqrt{1 - x^{2}}}{x^{6}} & \text{otherwise} \end{cases}\, dx$$
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1 / | | / _________ _________ _________ | | / 2 / 2 / 2 | | 2*I I*\/ -1 + x 2*I*\/ -1 + x I*\/ -1 + x I I 2 | |--------------- + -------------- - ---------------- - -------------- - ----------------- + ------------------ for x > 1 | | _________ 6 2 4 _________ _________ | | / 2 x 15*x 5*x 4 / 2 2 / 2 | |15*\/ -1 + x 5*x *\/ -1 + x 15*x *\/ -1 + x | < dx | | ________ ________ ________ | | / 2 / 2 / 2 | | 2 \/ 1 - x 2*\/ 1 - x \/ 1 - x 1 1 | | - -------------- + ----------- - ------------- - ----------- - ----------------- + ---------------- otherwise | | ________ 6 2 4 ________ ________ | | / 2 x 15*x 5*x 2 / 2 4 / 2 | \ 15*\/ 1 - x 15*x *\/ 1 - x 5*x *\/ 1 - x | / 0
$$\int\limits_{0}^{1} \begin{cases} \frac{2 i}{15 \sqrt{x^{2} - 1}} - \frac{2 i \sqrt{x^{2} - 1}}{15 x^{2}} + \frac{i}{15 x^{2} \sqrt{x^{2} - 1}} - \frac{i \sqrt{x^{2} - 1}}{5 x^{4}} - \frac{i}{5 x^{4} \sqrt{x^{2} - 1}} + \frac{i \sqrt{x^{2} - 1}}{x^{6}} & \text{for}\: x^{2} > 1 \\- \frac{2}{15 \sqrt{1 - x^{2}}} - \frac{2 \sqrt{1 - x^{2}}}{15 x^{2}} - \frac{1}{15 x^{2} \sqrt{1 - x^{2}}} - \frac{\sqrt{1 - x^{2}}}{5 x^{4}} + \frac{1}{5 x^{4} \sqrt{1 - x^{2}}} + \frac{\sqrt{1 - x^{2}}}{x^{6}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((2*i/(15*sqrt(-1 + x^2)) + i*sqrt(-1 + x^2)/x^6 - 2*i*sqrt(-1 + x^2)/(15*x^2) - i*sqrt(-1 + x^2)/(5*x^4) - i/(5*x^4*sqrt(-1 + x^2)) + i/(15*x^2*sqrt(-1 + x^2)), x^2 > 1), (-2/(15*sqrt(1 - x^2)) + sqrt(1 - x^2)/x^6 - 2*sqrt(1 - x^2)/(15*x^2) - sqrt(1 - x^2)/(5*x^4) - 1/(15*x^2*sqrt(1 - x^2)) + 1/(5*x^4*sqrt(1 - x^2)), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.