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