Sr Examen
Integral de sqrt((2sqrt(4+x)+1)/(2sqrt(4+x))) dx
Solución
Ha introducido
[src]
1 / | | _________________ | / _______ | / 2*\/ 4 + x + 1 | / --------------- dx | / _______ | \/ 2*\/ 4 + x | / 0
$$\int\limits_{0}^{1} \sqrt{\frac{2 \sqrt{x + 4} + 1}{2 \sqrt{x + 4}}}\, dx$$
Integral(sqrt((2*sqrt(4 + x) + 1)/((2*sqrt(4 + x)))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 5/4 ___ / ___ 4 _______\ 4 _______ 3/4 \ / ___ | 2*(4 + x) \/ 2 *asinh\\/ 2 *\/ 4 + x / \/ 4 + x 3*(4 + x) | | \/ 2 *|-------------------- - ---------------------------- + ---------------------- + ----------------------| | _________________ | _________________ 8 _________________ _________________| | / _______ | / _______ / _______ / _______ | | / 2*\/ 4 + x + 1 \\/ 1 + 2*\/ 4 + x 4*\/ 1 + 2*\/ 4 + x 2*\/ 1 + 2*\/ 4 + x / | / --------------- dx = C + ------------------------------------------------------------------------------------------------------------- | / _______ 2 | \/ 2*\/ 4 + x | /
$$\int \sqrt{\frac{2 \sqrt{x + 4} + 1}{2 \sqrt{x + 4}}}\, dx = C + \frac{\sqrt{2} \left(\frac{2 \left(x + 4\right)^{\frac{5}{4}}}{\sqrt{2 \sqrt{x + 4} + 1}} + \frac{3 \left(x + 4\right)^{\frac{3}{4}}}{2 \sqrt{2 \sqrt{x + 4} + 1}} + \frac{\sqrt[4]{x + 4}}{4 \sqrt{2 \sqrt{x + 4} + 1}} - \frac{\sqrt{2} \operatorname{asinh}{\left(\sqrt{2} \sqrt[4]{x + 4} \right)}}{8}\right)}{2}$$
Respuesta
[src]
/ ___ / ___ 4 ___\ 3/4 4 ___ \
___ | \/ 2 *asinh\\/ 2 *\/ 5 / 3*5 41*\/ 5 |
\/ 2 *|- ------------------------ + ------------------ + ------------------| / ____ ___ \
| 8 _____________ _____________| ___ |9*\/ 10 \/ 2 *asinh(2)|
| / ___ / ___ | \/ 2 *|-------- - --------------|
\ 2*\/ 1 + 2*\/ 5 4*\/ 1 + 2*\/ 5 / \ 4 8 /
---------------------------------------------------------------------------- - ---------------------------------
2 2
$$- \frac{\sqrt{2} \left(- \frac{\sqrt{2} \operatorname{asinh}{\left(2 \right)}}{8} + \frac{9 \sqrt{10}}{4}\right)}{2} + \frac{\sqrt{2} \left(- \frac{\sqrt{2} \operatorname{asinh}{\left(\sqrt{2} \sqrt[4]{5} \right)}}{8} + \frac{3 \cdot 5^{\frac{3}{4}}}{2 \sqrt{1 + 2 \sqrt{5}}} + \frac{41 \sqrt[4]{5}}{4 \sqrt{1 + 2 \sqrt{5}}}\right)}{2}$$
=
=
/ ___ / ___ 4 ___\ 3/4 4 ___ \
___ | \/ 2 *asinh\\/ 2 *\/ 5 / 3*5 41*\/ 5 |
\/ 2 *|- ------------------------ + ------------------ + ------------------| / ____ ___ \
| 8 _____________ _____________| ___ |9*\/ 10 \/ 2 *asinh(2)|
| / ___ / ___ | \/ 2 *|-------- - --------------|
\ 2*\/ 1 + 2*\/ 5 4*\/ 1 + 2*\/ 5 / \ 4 8 /
---------------------------------------------------------------------------- - ---------------------------------
2 2
$$- \frac{\sqrt{2} \left(- \frac{\sqrt{2} \operatorname{asinh}{\left(2 \right)}}{8} + \frac{9 \sqrt{10}}{4}\right)}{2} + \frac{\sqrt{2} \left(- \frac{\sqrt{2} \operatorname{asinh}{\left(\sqrt{2} \sqrt[4]{5} \right)}}{8} + \frac{3 \cdot 5^{\frac{3}{4}}}{2 \sqrt{1 + 2 \sqrt{5}}} + \frac{41 \sqrt[4]{5}}{4 \sqrt{1 + 2 \sqrt{5}}}\right)}{2}$$
sqrt(2)*(-sqrt(2)*asinh(sqrt(2)*5^(1/4))/8 + 3*5^(3/4)/(2*sqrt(1 + 2*sqrt(5))) + 41*5^(1/4)/(4*sqrt(1 + 2*sqrt(5))))/2 - sqrt(2)*(9*sqrt(10)/4 - sqrt(2)*asinh(2)/8)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.