求不定积分 sinxcosx/1+sinx^4 dx

∫ sinxcosx/(1+sin^4x) dx
= ∫ sinx/(1+sin^4x) d(sinx)
= ∫ 1/(1+sin^4x) d(1/2*sin²x)
= (1/2)∫ d(sin²x)/[1+(sin²x)²]
= (1/2)*arctan(sin²x) + C
公式∫ dx/(1+x²) = arctanx + C