sinx的3次方的不定积分怎么做 老哥们sinx的三次方不定积分有一部不知道 求解答
1/sinx\u76843\u6b21\u65b9\u7684\u4e0d\u5b9a\u79ef\u5206\u600e\u4e48\u7b97\uff0c\u6c42\u8fc7\u7a0b\u222b1/sin³x dx=(-1/2)cscx*cotx + (1/2)ln|cscx - cotx| + C\u3002C\u4e3a\u79ef\u5206\u5e38\u6570\u3002
\u89e3\u7b54\u8fc7\u7a0b\u5982\u4e0b\uff1a
\u222b1/sin³x dx
=\u222bcsc³x dx
=\u222bcscx*csc²x dx
=\u222bcscx d(-cotx)
=-cscx*cotx + \u222bcotx d(cscx)\uff0c\u5206\u90e8\u79ef\u5206\u6cd5
=-cscx*cotx + \u222bcotx*(-cscxcotx) dx
=-cscx*cotx - \u222bcscx*cot²x dx
=-cscx*cotx - \u222bcscx*(csc²x-1) dx\uff0c\u6052\u7b49\u5f0fcsc²x=1+cot²x
=-cscx*cotx - \u222bcsc³x dx + \u222bcscx dx\uff0c\u5c06-\u222bcsc³x dx\u79fb\u9879
\u22352\u222bcsc³x dx = -cscx*cotx + \u222bcscx dx\uff0c\u6ce8\u610f\u222bcscx dx = ln|cscx - cotx| + C
\u2234\u222bcsc³x dx = (-1/2)cscx*cotx + (1/2)ln|cscx - cotx| + C
\u6269\u5c55\u8d44\u6599\uff1a
\u5206\u90e8\u79ef\u5206\uff1a
(uv)'=u'v+uv'
\u5f97\uff1au'v=(uv)'-uv'
\u4e24\u8fb9\u79ef\u5206\u5f97\uff1a\u222b u'v dx=\u222b (uv)' dx - \u222b uv' dx
\u5373\uff1a\u222b u'v dx = uv - \u222b uv' d,\u8fd9\u5c31\u662f\u5206\u90e8\u79ef\u5206\u516c\u5f0f
\u4e5f\u53ef\u7b80\u5199\u4e3a\uff1a\u222b v du = uv - \u222b u dv
\u4e0d\u5b9a\u79ef\u5206\u7684\u516c\u5f0f
1\u3001\u222b a dx = ax + C\uff0ca\u548cC\u90fd\u662f\u5e38\u6570
2\u3001\u222b x^a dx = [x^(a + 1)]/(a + 1) + C\uff0c\u5176\u4e2da\u4e3a\u5e38\u6570\u4e14 a \u2260 -1
3\u3001\u222b 1/x dx = ln|x| + C
4\u3001\u222b a^x dx = (1/lna)a^x + C\uff0c\u5176\u4e2da > 0 \u4e14 a \u2260 1
5\u3001\u222b e^x dx = e^x + C
6\u3001\u222b cosx dx = sinx + C
7\u3001\u222b sinx dx = - cosx + C
8\u3001\u222b cotx dx = ln|sinx| + C = - ln|cscx| + C
d\uff08cosx\uff09=\uff08-sinx\uff09dx\uff0c\u7528\u7684\u77e5\u8bc6\u662f\u5fae\u5206\uff1ady=y\u2019dx
∫ (sinx)^3 dx = ∫ (sinx)^2 sinx dx= ∫ (1-(cosx)^2) (-1) d(cosx)
= - cosx +1/3 (cosx)^3 + C
还可以有别的计算方法，得到的结果外型上可能会有区别，但都是对的（因为三角函数加上或者减去常数会变成不同的形式）。
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