Sr Examen
Integral de x^(1/2)/(1-x^(1/4)) dx
Solución
Ha introducido
[src]
1 / | | ___ | \/ x | --------- dx | 4 ___ | 1 - \/ x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x}}{1 - \sqrt[4]{x}}\, dx$$
Integral(sqrt(x)/(1 - x^(1/4)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | ___ 3/4 5/4 | \/ x 4 ___ / 4 ___\ ___ 4*x 4*x | --------- dx = C - x - 4*\/ x - 4*log\-1 + \/ x / - 2*\/ x - ------ - ------ | 4 ___ 3 5 | 1 - \/ x | /
$$\int \frac{\sqrt{x}}{1 - \sqrt[4]{x}}\, dx = C - \frac{4 x^{\frac{5}{4}}}{5} - \frac{4 x^{\frac{3}{4}}}{3} - 4 \sqrt[4]{x} - 2 \sqrt{x} - x - 4 \log{\left(\sqrt[4]{x} - 1 \right)}$$
Gráfica
Respuesta
[src]
1 / | | / 1 1 1 4 ___ 1 4 ___ | |-1 - ---- - ----- - ----- - \/ x - ----------------- for \/ x > 1 | | 3/4 ___ 4 ___ 3/4 / 4 ___\ | | x \/ x \/ x x *\-1 + \/ x / | < dx | | 1 1 1 4 ___ 1 | |-1 - ---- - ----- - ----- - \/ x + ---------------- otherwise | | 3/4 ___ 4 ___ 3/4 / 4 ___\ | \ x \/ x \/ x x *\1 - \/ x / | / 0
$$\int\limits_{0}^{1} \begin{cases} - \sqrt[4]{x} - 1 - \frac{1}{\sqrt{x}} - \frac{1}{\sqrt[4]{x}} - \frac{1}{x^{\frac{3}{4}}} - \frac{1}{x^{\frac{3}{4}} \left(\sqrt[4]{x} - 1\right)} & \text{for}\: \sqrt[4]{x} > 1 \\- \sqrt[4]{x} - 1 - \frac{1}{\sqrt{x}} - \frac{1}{\sqrt[4]{x}} - \frac{1}{x^{\frac{3}{4}}} + \frac{1}{x^{\frac{3}{4}} \left(1 - \sqrt[4]{x}\right)} & \text{otherwise} \end{cases}\, dx$$
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1 / | | / 1 1 1 4 ___ 1 4 ___ | |-1 - ---- - ----- - ----- - \/ x - ----------------- for \/ x > 1 | | 3/4 ___ 4 ___ 3/4 / 4 ___\ | | x \/ x \/ x x *\-1 + \/ x / | < dx | | 1 1 1 4 ___ 1 | |-1 - ---- - ----- - ----- - \/ x + ---------------- otherwise | | 3/4 ___ 4 ___ 3/4 / 4 ___\ | \ x \/ x \/ x x *\1 - \/ x / | / 0
$$\int\limits_{0}^{1} \begin{cases} - \sqrt[4]{x} - 1 - \frac{1}{\sqrt{x}} - \frac{1}{\sqrt[4]{x}} - \frac{1}{x^{\frac{3}{4}}} - \frac{1}{x^{\frac{3}{4}} \left(\sqrt[4]{x} - 1\right)} & \text{for}\: \sqrt[4]{x} > 1 \\- \sqrt[4]{x} - 1 - \frac{1}{\sqrt{x}} - \frac{1}{\sqrt[4]{x}} - \frac{1}{x^{\frac{3}{4}}} + \frac{1}{x^{\frac{3}{4}} \left(1 - \sqrt[4]{x}\right)} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-1 - 1/x^(3/4) - 1/sqrt(x) - 1/x^(1/4) - x^(1/4) - 1/(x^(3/4)*(-1 + x^(1/4))), x^(1/4) > 1), (-1 - 1/x^(3/4) - 1/sqrt(x) - 1/x^(1/4) - x^(1/4) + 1/(x^(3/4)*(1 - x^(1/4))), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.