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Resolución de integrales/ x^(3/2)/ cos^2/ x^(1/2)/ x^(1/2)*cos^2(x^(3/2))

Integral de x^(1/2)*cos^2(x^(3/2)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   3/2                   
 pi                      
   /                     
  |                      
  |     ___    2/ 3/2\   
  |   \/ x *cos \x   / dx
  |                      
 /                       
 0
∫0π32xcos⁡2(x32) dx\int\limits_{0}^{\pi^{\frac{3}{2}}} \sqrt{x} \cos^{2}{\left(x^{\frac{3}{2}} \right)}\, dx 
Integral(sqrt(x)*cos(x^(3/2))^2, (x, 0, pi^(3/2)))
Respuesta (Indefinida) [src] 
  /                                                                                 
 |                            3/2    2/ 3/2\    3/2    2/ 3/2\      / 3/2\    / 3/2\
 |   ___    2/ 3/2\          x   *cos \x   /   x   *sin \x   /   cos\x   /*sin\x   /
 | \/ x *cos \x   / dx = C + --------------- + --------------- + -------------------
 |                                  3                 3                   3         
/
∫xcos⁡2(x32) dx=C+x32sin⁡2(x32)3+x32cos⁡2(x32)3+sin⁡(x32)cos⁡(x32)3\int \sqrt{x} \cos^{2}{\left(x^{\frac{3}{2}} \right)}\, dx = C + \frac{x^{\frac{3}{2}} \sin^{2}{\left(x^{\frac{3}{2}} \right)}}{3} + \frac{x^{\frac{3}{2}} \cos^{2}{\left(x^{\frac{3}{2}} \right)}}{3} + \frac{\sin{\left(x^{\frac{3}{2}} \right)} \cos{\left(x^{\frac{3}{2}} \right)}}{3}
Simplificar
Gráfica
0.00.51.01.52.02.53.03.54.04.55.05.55-5
Trazar el gráfico f(x)
Respuesta [src] 
                       /  9/4\                         /  9/4     \                            /  9/4\                       /  9/4\ /  9/4     \                /  9/4\ /  9/4     \   
                      3|pi   |                         |pi        |                            |pi   |                      4|pi   | |pi        |               2|pi   | |pi        |   
                 2*tan |-----|                       2*|----- - pi|                       2*tan|-----|                 2*tan |-----|*|----- - pi|          4*tan |-----|*|----- - pi|   
2*pi                   \  2  /                         \  2       /                            \  2  /                       \  2  / \  2       /                \  2  / \  2       /   
---- - --------------------------------- + --------------------------------- + --------------------------------- + --------------------------------- + ---------------------------------
 3               /  9/4\         /  9/4\             /  9/4\         /  9/4\             /  9/4\         /  9/4\             /  9/4\         /  9/4\             /  9/4\         /  9/4\
                4|pi   |        2|pi   |            4|pi   |        2|pi   |            4|pi   |        2|pi   |            4|pi   |        2|pi   |            4|pi   |        2|pi   |
       3 + 3*tan |-----| + 6*tan |-----|   3 + 3*tan |-----| + 6*tan |-----|   3 + 3*tan |-----| + 6*tan |-----|   3 + 3*tan |-----| + 6*tan |-----|   3 + 3*tan |-----| + 6*tan |-----|
                 \  2  /         \  2  /             \  2  /         \  2  /             \  2  /         \  2  /             \  2  /         \  2  /             \  2  /         \  2  /
−2tan⁡3(π942)3tan⁡4(π942)+6tan⁡2(π942)+3+2(−π+π942)tan⁡4(π942)3tan⁡4(π942)+6tan⁡2(π942)+3+2tan⁡(π942)3tan⁡4(π942)+6tan⁡2(π942)+3+4(−π+π942)tan⁡2(π942)3tan⁡4(π942)+6tan⁡2(π942)+3+2(−π+π942)3tan⁡4(π942)+6tan⁡2(π942)+3+2π3- \frac{2 \tan^{3}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right) \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \tan{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{4 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right) \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right)}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \pi}{3} 
=
= 
                       /  9/4\                         /  9/4     \                            /  9/4\                       /  9/4\ /  9/4     \                /  9/4\ /  9/4     \   
                      3|pi   |                         |pi        |                            |pi   |                      4|pi   | |pi        |               2|pi   | |pi        |   
                 2*tan |-----|                       2*|----- - pi|                       2*tan|-----|                 2*tan |-----|*|----- - pi|          4*tan |-----|*|----- - pi|   
2*pi                   \  2  /                         \  2       /                            \  2  /                       \  2  / \  2       /                \  2  / \  2       /   
---- - --------------------------------- + --------------------------------- + --------------------------------- + --------------------------------- + ---------------------------------
 3               /  9/4\         /  9/4\             /  9/4\         /  9/4\             /  9/4\         /  9/4\             /  9/4\         /  9/4\             /  9/4\         /  9/4\
                4|pi   |        2|pi   |            4|pi   |        2|pi   |            4|pi   |        2|pi   |            4|pi   |        2|pi   |            4|pi   |        2|pi   |
       3 + 3*tan |-----| + 6*tan |-----|   3 + 3*tan |-----| + 6*tan |-----|   3 + 3*tan |-----| + 6*tan |-----|   3 + 3*tan |-----| + 6*tan |-----|   3 + 3*tan |-----| + 6*tan |-----|
                 \  2  /         \  2  /             \  2  /         \  2  /             \  2  /         \  2  /             \  2  /         \  2  /             \  2  /         \  2  /
−2tan⁡3(π942)3tan⁡4(π942)+6tan⁡2(π942)+3+2(−π+π942)tan⁡4(π942)3tan⁡4(π942)+6tan⁡2(π942)+3+2tan⁡(π942)3tan⁡4(π942)+6tan⁡2(π942)+3+4(−π+π942)tan⁡2(π942)3tan⁡4(π942)+6tan⁡2(π942)+3+2(−π+π942)3tan⁡4(π942)+6tan⁡2(π942)+3+2π3- \frac{2 \tan^{3}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right) \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \tan{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{4 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right) \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right)}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \pi}{3} 
2*pi/3 - 2*tan(pi^(9/4)/2)^3/(3 + 3*tan(pi^(9/4)/2)^4 + 6*tan(pi^(9/4)/2)^2) + 2*(pi^(9/4)/2 - pi)/(3 + 3*tan(pi^(9/4)/2)^4 + 6*tan(pi^(9/4)/2)^2) + 2*tan(pi^(9/4)/2)/(3 + 3*tan(pi^(9/4)/2)^4 + 6*tan(pi^(9/4)/2)^2) + 2*tan(pi^(9/4)/2)^4*(pi^(9/4)/2 - pi)/(3 + 3*tan(pi^(9/4)/2)^4 + 6*tan(pi^(9/4)/2)^2) + 4*tan(pi^(9/4)/2)^2*(pi^(9/4)/2 - pi)/(3 + 3*tan(pi^(9/4)/2)^4 + 6*tan(pi^(9/4)/2)^2)
Respuesta numérica [src] 
4.53182410805293
4.53182410805293

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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