作业帮求下列不定积分.求详解（1）∫[(cos 2x)／(cos x﹢sin x)]dx; (2) ∫cot²xdx; (3) ∫{(1+2x²)／[x²(1+x²)]}dx; (4) ∫sin²(x／2)dx; (5) ∫[(cos2x)／(sin²xcos²x)]dx; (6) ∫[e^(x-4)]dx;求解
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![求下列不定积分.求详解（1）∫[(cos 2x)／(cos x﹢sin x)]dx; (2) ∫cot²xdx; (3) ∫{(1+2x²)／[x²(1+x²)]}dx; (4) ∫sin²(x／2)dx; (5) ∫[(cos2x)／(sin²xcos²x)]dx; (6) ∫[e^(x-4)]dx;求解](/uploads/image/z/11470561-25-1.jpg?t=%E6%B1%82%E4%B8%8B%E5%88%97%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86.%E6%B1%82%E8%AF%A6%E8%A7%A3%EF%BC%881%EF%BC%89%E2%88%AB%5B%28cos+2x%29%EF%BC%8F%28cos+x%EF%B9%A2sin+x%29%5Ddx%3B++%282%29++%E2%88%ABcot%26%23178%3Bxdx%3B++%283%29++%E2%88%AB%7B%281%2B2x%26%23178%3B%29%EF%BC%8F%5Bx%26%23178%3B%281%2Bx%26%23178%3B%29%5D%7Ddx%3B++%284%29++%E2%88%ABsin%26%23178%3B%28x%EF%BC%8F2%29dx%3B++%285%29++%E2%88%AB%5B%28cos2x%29%EF%BC%8F%28sin%26%23178%3Bxcos%26%23178%3Bx%29%5Ddx%3B++%286%29++%E2%88%AB%5Be%5E%28x-4%29%5Ddx%3B%E6%B1%82%E8%A7%A3)
求下列不定积分.求详解（1）∫[(cos 2x)／(cos x﹢sin x)]dx; (2) ∫cot²xdx; (3) ∫{(1+2x²)／[x²(1+x²)]}dx; (4) ∫sin²(x／2)dx; (5) ∫[(cos2x)／(sin²xcos²x)]dx; (6) ∫[e^(x-4)]dx;求解
求下列不定积分.求详解
（1）∫[(cos 2x)／(cos x﹢sin x)]dx;
(2) ∫cot²xdx;
(3) ∫{(1+2x²)／[x²(1+x²)]}dx;
(4) ∫sin²(x／2)dx;
(5) ∫[(cos2x)／(sin²xcos²x)]dx;
(6) ∫[e^(x-4)]dx;
求解答啊。。。。。。。。。。。。。。。。谢谢啦
求下列不定积分.求详解（1）∫[(cos 2x)／(cos x﹢sin x)]dx; (2) ∫cot²xdx; (3) ∫{(1+2x²)／[x²(1+x²)]}dx; (4) ∫sin²(x／2)dx; (5) ∫[(cos2x)／(sin²xcos²x)]dx; (6) ∫[e^(x-4)]dx;求解
cos2x=cos²x-sin²x=(cosx+sinx)(cosx-sinx)
∫(cosx-sinx)dx=sinx+cosx+C
∫cot²xdx=∫(csc²x-1)dx=-cotx-x+C
x=tanθ,dx=sec²θdθ
∫(1+2tan²θ)sec²θdθ/tan²θsec²θ
=∫(cotθ+2)dθ=ln|sinθ|+2θ+C=ln|x/√(1+x²)|+2arctanx+C
∫sin²(x/2)dx=(1/2)∫(1-cosx)dx=(x-sinx)/2+C
∫cos2xdx/(sinxcosx)²=4∫cos2xdx/sin²2x
=2∫d(sin2x)/sin²2x=-2/sin2x+C
∫[e^(x-4)]dx=e^(x-4)+C