20163315 치환적분

2274 days 전, qogustlr7 작성

치환적분 24.
var('t') f(t)=1/(cos(t)^2*sqrt(1+tan(t))) integral(f(t),t) 
        
2*sqrt(tan(t) + 1)
2*sqrt(tan(t) + 1)

치환적분 25.
f(x)=sqrt(cot(x))*csc(x)^2 integral(f(x),x) 
        
-2/3*cot(x)^(3/2)
-2/3*cot(x)^(3/2)

치환적분 26.
var('t') f(t)=sin(t)*sec(cos(t))^2 integral(f(t),t) 
        
-tan(cos(t))
-tan(cos(t))

치환적분 81.
f(x)=1/(x*sqrt(log(x))) integral(f(x), x, e, e^4) 
        
2
2

치환적분 82.
f(x)=x*e^(-x^2) integral(f(x), x, 0, 1) 
        
-1/2*e^(-1) + 1/2
-1/2*e^(-1) + 1/2
var('z') f(z)=(e^(z)+1)/(e^(z)+z) integral(f(z), z, 0, 1) 
        
integrate((e^z + 1)/(z + e^z), z, 0, 1)
integrate((e^z + 1)/(z + e^z), z, 0, 1)
f(x)=((e^(x)+1))/((e^(x)+x)) integral(f(x), x, 0, 1) 
        
integrate((e^x + 1)/(x + e^x), x, 0, 1)
integrate((e^x + 1)/(x + e^x), x, 0, 1)

치환적분 84.
f(x)=arcsin(x)/sqrt(1-x^2) integral(f(x), x, 0, 1/2) 
        
1/72*pi^2
1/72*pi^2