if we are integrating trig functions in cubic or squared form , do we have to convert them into linear form first?

And can anyone tell me the steps of differential equations?

Thanks

Question

if we are integrating trig functions in cubic or squared form , do we have to convert them into linear form first? 

And can anyone tell me the steps of differential equations?

Thanks

anonymous · Answer

Like using identities to convert them into linear form

callisto · Answer

Usually, yes, but it depends
For example, for $$\int cos^2x dx$$$$=\int \frac{cos2x+1}{2} dx$$$$=\frac{1}{2} \int cos2x+1 dx = \frac{1}{4}sin2x + \frac{x}{2}+C$$

callisto · Answer

But when you're integrating 
$$\int sin^3xcos^3x dx$$ That's another story
$$\int sin^3xcos^3x dx$$$$=\int sin^3xcos^2xcosx dx$$$$=\int sin^3x(1-sin^2x) d(sinx)$$$$=\int sin^3x-sin^5x d(sinx)$$$$=\frac{sin^4x}{4}-\frac{sin^6x}{6} +C$$