Sr Examen
Integral de sqrt(1+(1/2x))*(-sqrt(2x)) dx
Solución
Ha introducido
[src]
3/2 / | | _______ | / x / _____\ | / 1 + - *\-\/ 2*x / dx | \/ 2 | / 0
$$\int\limits_{0}^{\frac{3}{2}} - \sqrt{2 x} \sqrt{\frac{x}{2} + 1}\, dx$$
Integral(sqrt(1 + x/2)*(-sqrt(2*x)), (x, 0, 3/2))
Respuesta (Indefinida)
[src]
// / ___ _______\ _______ 5/2 3/2 \
/ || |\/ 2 *\/ 2 + x | \/ 2 + x (2 + x) 3*(2 + x) |2 + x| |
| || - acosh|---------------| + --------- + ---------- - ------------ for ------- > 1|
| _______ || \ 2 / ___ ___ ___ 2 |
| / x / _____\ || \/ x 2*\/ x 2*\/ x |
| / 1 + - *\-\/ 2*x / dx = C - |< |
| \/ 2 || / ___ _______\ _______ 5/2 3/2 |
| || |\/ 2 *\/ 2 + x | I*\/ 2 + x I*(2 + x) 3*I*(2 + x) |
/ ||I*asin|---------------| - ----------- - ------------ + -------------- otherwise |
|| \ 2 / ____ ____ ____ |
\\ \/ -x 2*\/ -x 2*\/ -x /
$$\int - \sqrt{2 x} \sqrt{\frac{x}{2} + 1}\, dx = C - \begin{cases} - \operatorname{acosh}{\left(\frac{\sqrt{2} \sqrt{x + 2}}{2} \right)} + \frac{\left(x + 2\right)^{\frac{5}{2}}}{2 \sqrt{x}} - \frac{3 \left(x + 2\right)^{\frac{3}{2}}}{2 \sqrt{x}} + \frac{\sqrt{x + 2}}{\sqrt{x}} & \text{for}\: \frac{\left|{x + 2}\right|}{2} > 1 \\i \operatorname{asin}{\left(\frac{\sqrt{2} \sqrt{x + 2}}{2} \right)} - \frac{i \left(x + 2\right)^{\frac{5}{2}}}{2 \sqrt{- x}} + \frac{3 i \left(x + 2\right)^{\frac{3}{2}}}{2 \sqrt{- x}} - \frac{i \sqrt{x + 2}}{\sqrt{- x}} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
/ / ___\\
| ___ |\/ 7 ||
| ____ \/ 2 *acosh|-----||
___ |5*\/ 42 \ 2 /|
-\/ 2 *|-------- - ------------------|
\ 16 2 /
$$- \sqrt{2} \left(- \frac{\sqrt{2} \operatorname{acosh}{\left(\frac{\sqrt{7}}{2} \right)}}{2} + \frac{5 \sqrt{42}}{16}\right)$$
=
=
/ / ___\\
| ___ |\/ 7 ||
| ____ \/ 2 *acosh|-----||
___ |5*\/ 42 \ 2 /|
-\/ 2 *|-------- - ------------------|
\ 16 2 /
$$- \sqrt{2} \left(- \frac{\sqrt{2} \operatorname{acosh}{\left(\frac{\sqrt{7}}{2} \right)}}{2} + \frac{5 \sqrt{42}}{16}\right)$$
-sqrt(2)*(5*sqrt(42)/16 - sqrt(2)*acosh(sqrt(7)/2)/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.