【解析】 $$ \frac{1}{1+ \tan x} $$ $$ \frac { 1 } { 1 + \tan x } $$ $$ = \frac{\cos x}{\cos x+ \sin x} $$ $$ = \frac{(\cos x+ \sin x)+(\cos x- \sin x)}{\cos x+ \sin x}. \frac{1}{2} \\ = \frac{1}{2}+ \frac{1}{2}\cdot \frac{\cos...
答案: 解:令$$ t= \tan \frac{x}{2} $$,$$ dx= \frac{2}{1+t^{2}} $$dt $$ \cosx= \frac{1-t^{2}}{1+t^{2}} $$,代入 $$ \int \frac{1}{5+ \cos x}dx \\ = \int \frac{1}{5+ \frac{1-t^{2}}{1+t^{2}}}\cdot \frac{2}{1+t^{2}}dt \\ = \int \...
Calculate the antiderivative: {eq}\displaystyle \int \frac{1}{2x^5} \ dx {/eq}Question:Calculate the antiderivative: {eq}\displaystyle \int \frac{1}{2x^5} \ dx {/eq}Antiderivative:An antiderivative is also known as an indefinite integral, primitive integral, or inverse derivative. If an...
Answer to: Integrate the following function \int \frac {5x-1}{x+1}dx By signing up, you'll get thousands of step-by-step solutions to your...
Answer to: Integrate. \int \frac{x + 5}{(x + 1)^{2}(x^{2} + 4x + 5)} dx By signing up, you'll get thousands of step-by-step solutions to your...
\int _{ \frac {1}{e} }^{ e } \dfrac {1}{x}dx=\ln x |_{ \frac {1}{e} }^{ e }=\ln e-\ln \dfrac {1}{e}=2.故答案为:2 根据积分计算公式,求出被积函数 \dfrac {1}{x}的原函数,再根据微积分基本定理加以计算,即可得到本题答案.本题求函数 \dfrac {1}{x}...
(但这样做下去较繁,换个解法) 另 ∫{1/[x(1+x^6)]}dx = ∫{x/[x²(1+x^6)]}dx = (1/2)∫{1/{x²[1+(x²)³]}}d(x²) = (1/2)∫{1/[u(1+u³)]}du (u=x²)而 1/[u(1+u³)] = 1/[u(u+1)(u²-u+1)],然后用待定系数法,…… ...
Answer to: Find the indefinite integral. \int \frac{1}{5x^7} dx By signing up, you'll get thousands of step-by-step solutions to your homework...
Answer to: Find the indefinite integral: \int \frac{x^5}{1-x^6} dx By signing up, you'll get thousands of step-by-step solutions to your homework...
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