Question

find Intgrl 1/((sinx)3+(cosx)3)

Answer 1

really?
http://www.wolframalpha.com/input/?i=integrate+1%2F%28cos^3%28x%29%2Bsin^3%28x%29%29

Answer 2

Using MATLAB:

syms x;int(1/(3*sin(x)+3*cos(x)))

ans =

1/3*2^(1/2)*atanh(1/4*(2*tan(1/2*x)-2)*2^(1/2))

Answer 3

But if you mean sin(x)^3 and cos(x)^3

syms x;int(1/(sin(x)^3+cos(x)^3))

ans =

1/3*i*log(tan(1/2*x)^2+(1-i)*tan(1/2*x)+i)-1/3*i*log(tan(1/2*x)^2+(1+i)*tan(1/2*x)-i)+2/3*2^(1/2)*atanh(1/4*(2*tan(1/2*x)-2)*2^(1/2))