ejercicios segunda parte

302 days ago by 1234christian5689@tecpabellon

#20 julio 2011 
       
1 f=((5*x)*(2*x^2+1)^-3) f.integral(x) 
        
-5/8/(2*x^2 + 1)^2
-5/8/(2*x^2 + 1)^2
2 f=((3*x)*(2)) f.integral(x) 
        
3*x^2
3*x^2
3 f=(1)/(x+(x)^1/2) f.integral(x) 
        
2/3*log(x)
2/3*log(x)
4 f=((x^2)*(x+1)^1/2) f.integral(x) 
        
1/8*x^4 + 1/6*x^3
1/8*x^4 + 1/6*x^3
5 f=((x^2)/(1-2*x^3)) f.integral(x) 
        
-1/6*log(2*x^3 - 1)
-1/6*log(2*x^3 - 1)
6 f=(x^3+x^2-4/x^2) f.integral(x) 
        
1/4*x^4 + 1/3*x^3 + 4/x
1/4*x^4 + 1/3*x^3 + 4/x
7 f=((1+tan(x))^2) f.integral(x) 
        
2*log(sec(x)) + tan(x)
2*log(sec(x)) + tan(x)
#21 de julio 2011 
       
1 f=((5*x-2)^-1/2) f.integral(x) 
        
1/10*log(5*x - 2)
1/10*log(5*x - 2)
2 f=((x)/(x+1)^1/2) f.integral(x) 
        
1/2*x - 1/2*log(x + 1)
1/2*x - 1/2*log(x + 1)
3 f=((x)*((x+1)^1/2)) f.integral(x) 
        
1/6*x^3 + 1/4*x^2
1/6*x^3 + 1/4*x^2
4 f=((x)*(sin(x))) f.integral(x) 
        
-x*cos(x) + sin(x)
-x*cos(x) + sin(x)
5 f=((x^2)*(log(x))) f.integral(x) 
        
1/3*x^3*log(x) - 1/9*x^3
1/3*x^3*log(x) - 1/9*x^3
6 f=((x)*(e^(6*x))) f.integral(x) 
        
1/36*(6*x - 1)*e^(6*x)
1/36*(6*x - 1)*e^(6*x)
7 f=((x^5)*((x^3+1)^1/2)) f.integral(x) 
        
1/18*x^9 + 1/12*x^6
1/18*x^9 + 1/12*x^6
#22 julio 2011 
       
1 f=((x^2)*(e^-x)) f.integral(x) 
        
-(x^2 + 2*x + 2)*e^(-x)
-(x^2 + 2*x + 2)*e^(-x)
2 f=((x^3)*(x^2)*(x^3+1)^1/2) f.integral(x) 
        
1/18*x^9 + 1/12*x^6
1/18*x^9 + 1/12*x^6
3 var('w') f=((w^2)*(sin(10w))) f.integral(w) 
        
Traceback (click to the left of this block for traceback)
...
SyntaxError: invalid syntax
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_4.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("Mwp2YXIoJ3cnKQpmPSgod14yKSooc2luKDEwdykpKQpmLmludGVncmFsKHcp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpaa0kmf/___code___.py", line 5
    f=((w**_sage_const_2 )*(sin(10w)))
                                  ^
SyntaxError: invalid syntax
4 f=((x^2)*(sin(x))) f.integral(x) 
        
-(x^2 - 2)*cos(x) + 2*x*sin(x)
-(x^2 - 2)*cos(x) + 2*x*sin(x)
5 var('t') f=((3*t+5)*(cos(t/4))) f.integral(t) 
        
12*t*sin(1/4*t) + 20*sin(1/4*t) + 48*cos(1/4*t)
12*t*sin(1/4*t) + 20*sin(1/4*t) + 48*cos(1/4*t)
#25 julio 2011 
       
1 f=((1+x^2)^-1/2) f.integral(x) 
        
1/2*arctan(x)
1/2*arctan(x)
2 f=((1-x^2)^(-1/2)) f.integral(x) 
        
arcsin(x)
arcsin(x)
3 f=((x)*(x^2-1)^(-1/2)) f.integral(x) 
        
sqrt(x^2 - 1)
sqrt(x^2 - 1)
4 f=((4-x^2)^(-1/2)) f.integral(x) 
        
arcsin(1/2*x)
arcsin(1/2*x)
5 f=(4/(25-16*x^2)^(1/2)) f.integral(x) 
        
arcsin(4/5*x)
arcsin(4/5*x)
6 f=((4*x^2+9)^(1/2)) f.integral(x) 
        
1/2*sqrt(4*x^2 + 9)*x + 9/4*arcsinh(2/3*x)
1/2*sqrt(4*x^2 + 9)*x + 9/4*arcsinh(2/3*x)
7 f=((x)*(4*x^2-9)^(-1/2)) f.integral(x) 
        
1/4*sqrt(4*x^2 - 9)
1/4*sqrt(4*x^2 - 9)
8 f=(x^2/(1-x^6)^(1/2)) f.integral(x) 
        
-1/3*arctan(sqrt(-x^6 + 1)/x^3)
-1/3*arctan(sqrt(-x^6 + 1)/x^3)
9 f=((x^4+3)^(1/2)) f.integral(x) 
        
integrate(sqrt(x^4 + 3), x)
integrate(sqrt(x^4 + 3), x)
10 f=(((4)*((x+2)^1/2))^(1/2)) f.integral(x) 
        
1/3*(2*x + 4)^(3/2)
1/3*(2*x + 4)^(3/2)
11 f=((sinxtanx/9+4sec^2*x)) f.integral(x) 
        
Traceback (click to the left of this block for traceback)
...
SyntaxError: invalid syntax
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_16.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("MTEKZj0oKHNpbnh0YW54LzkrNHNlY14yKngpKQpmLmludGVncmFsKHgp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmp0si_KC/___code___.py", line 4
    f=((sinxtanx/_sage_const_9 +4sec**_sage_const_2 *x))
                                   ^
SyntaxError: invalid syntax
12 f=(x+3/(1-x^2)^(1/2)) f.integral(x) 
        
1/2*x^2 + 3*arcsin(x)
1/2*x^2 + 3*arcsin(x)
13 f=(1-x^2)^(1/2) f.integral(x) 
        
1/2*sqrt(-x^2 + 1)*x + 1/2*arcsin(x)
1/2*sqrt(-x^2 + 1)*x + 1/2*arcsin(x)
14 f=(2*x+7/(x^2+9)^(1/2)) f.integral(x) 
        
x^2 + 7*arcsinh(1/3*x)
x^2 + 7*arcsinh(1/3*x)
15 f=(x^2+10*x+30)^(1/2) f.integral(x) 
        
1/2*sqrt(x^2 + 10*x + 30)*x + 5/2*sqrt(x^2 + 10*x + 30) +
5/2*arcsinh(1/5*(x + 5)*sqrt(5))
1/2*sqrt(x^2 + 10*x + 30)*x + 5/2*sqrt(x^2 + 10*x + 30) + 5/2*arcsinh(1/5*(x + 5)*sqrt(5))