Sr Examen
Integral de Cos(ax)/(b+sen(ax))^(-1/2) dx
Solución
Ha introducido
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1 / | | cos(a*x) | ------------------ dx | / 1 \ | |----------------| | | ______________| | \\/ b + sin(a*x) / | / 0
$$\int\limits_{0}^{1} \frac{\cos{\left(a x \right)}}{\frac{1}{\sqrt{b + \sin{\left(a x \right)}}}}\, dx$$
Integral(cos(a*x)/1/sqrt(b + sin(a*x)), (x, 0, 1))
Respuesta (Indefinida)
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/ // 3/2 \ | ||2*(b + sin(a*x)) | | cos(a*x) ||------------------- for a != 0| | ------------------ dx = C + |< 3*a | | / 1 \ || | | |----------------| || ___ | | | ______________| \\ x*\/ b otherwise / | \\/ b + sin(a*x) / | /
$$\int \frac{\cos{\left(a x \right)}}{\frac{1}{\sqrt{b + \sin{\left(a x \right)}}}}\, dx = C + \begin{cases} \frac{2 \left(b + \sin{\left(a x \right)}\right)^{\frac{3}{2}}}{3 a} & \text{for}\: a \neq 0 \\\sqrt{b} x & \text{otherwise} \end{cases}$$
Respuesta
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/ 3/2 ____________ ____________ | 2*b 2*b*\/ b + sin(a) 2*\/ b + sin(a) *sin(a) |- ------ + ------------------ + ----------------------- for And(a > -oo, a < oo, a != 0) < 3*a 3*a 3*a | | ___ \ \/ b otherwise
$$\begin{cases} - \frac{2 b^{\frac{3}{2}}}{3 a} + \frac{2 b \sqrt{b + \sin{\left(a \right)}}}{3 a} + \frac{2 \sqrt{b + \sin{\left(a \right)}} \sin{\left(a \right)}}{3 a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\sqrt{b} & \text{otherwise} \end{cases}$$
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/ 3/2 ____________ ____________ | 2*b 2*b*\/ b + sin(a) 2*\/ b + sin(a) *sin(a) |- ------ + ------------------ + ----------------------- for And(a > -oo, a < oo, a != 0) < 3*a 3*a 3*a | | ___ \ \/ b otherwise
$$\begin{cases} - \frac{2 b^{\frac{3}{2}}}{3 a} + \frac{2 b \sqrt{b + \sin{\left(a \right)}}}{3 a} + \frac{2 \sqrt{b + \sin{\left(a \right)}} \sin{\left(a \right)}}{3 a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\sqrt{b} & \text{otherwise} \end{cases}$$
Piecewise((-2*b^(3/2)/(3*a) + 2*b*sqrt(b + sin(a))/(3*a) + 2*sqrt(b + sin(a))*sin(a)/(3*a), (a > -oo)∧(a < oo)∧(Ne(a, 0))), (sqrt(b), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.