nsh1

integral of sin(x)/(sin(x)+cos(x))

(%i1)

f(x):=sin(x)/(sin(x)+cos(x));

Result

(%i2)

integrate(f(x),x,0,%pi/2);

Result

not easy

(%i3)

wxplot2d([f(x),1/2], [x,0,%pi/2])$

Result

symmetrical about (%pi/4,1/2)

(%i4)

(f(%pi/4+x)+f(%pi/4-x))/2;

Result

(%i5)

trigexpand(%);

Result

(%i6)

ratsimp(%);

Result

y=f(x) is symmetrical about (a,b):2b-y=f(2a-x)

(%i7)

1-f(%pi/2-x);

Result

(%i8)

ratsimp(%);

Result

t=tan(x/2)

(%i9)

integrate(4*t/(2*t+1-t^2)/(1+t^2),t,0,1);

Result

actually

(%i10)

partfrac((4*t)/(2*t+1-t^2)/(t^2+1), t);

Result

(%i11)

integrate((1-t)/(t^2-2*t-1),t,0,1);

Result

(%i12)

integrate(t/(t^2+1)+1/(t^2+1),t,0,1);

Result

Created with wxMaxima.