( (ln)(x)dx) 相关知识点: 试题来源: 解析 Since ( d) is constant with respect to ( x), move ( d) out of the integral.( d∫ (ln)(x)xdx)Integrate by parts using the formula( ∫ udv=uv-∫ vdu), where ( u=(ln)(x)) and ( dv=x).( d((ln)(x)(1/2x^2)-∫ 1/2x^...
Answer to: Evaluate the integral \int \frac{\cos(\ln 2x)}{x} \,dx By signing up, you'll get thousands of step-by-step solutions to your homework...
(b) integral ln (x^2 + 1) dx. Evaluate the integral. integral {e^{4 + 9 ln x / {square root {1 - x^{20} dx Evaluate the integral. integral 0^1 integral square root 3 z ^1 integral 0^ ln 3 fraction pi e^2x sin pi y...
\int_{0}^{1}x^{c{x}^a}dx=\int_{0}^{1}1+cx^a\ln x+\frac{1}{2!}c^2x^{2a}(\ln x)^2+\frac{1}{3!}c^3x^{3a}(\ln x)^3+...dx 然后再对单项分别进行积分 \int_{0}^{1}x^{c{x}^a}dx=\int_{0}^{1}dx+c\int_{0}^{1}x^a\ln xdx+\frac{c^2}{2!}\in...
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\int (x+1)^2dx=\int x^2+2x+1dx=\frac{1}{3}x^3+x^2+x+C 法二:换元法令t=x+1 , \frac{dt}{dx}=1\Rightarrow dt=dx,把所有的 x 都用t 来代替,于是 \int (x+1)^2dx=\int t^2 dt=\frac{1}{3}t^3=\frac{1}{3}(x+1)^3+C。 我们可以发现通过代换这样积分就简单了很多...
∫1√v2+a2dv=ln|v+√v2+a2|+Cwhere a=3. Thus, we get:I2=ln|v+√v2+9|+C2=ln|(x+1)+√(x+1)2+9|+C2 Step 4: Combine the ResultsNow, we combine both integrals:∫2x+3√x2+2x+10dx=I1+I2Substituting back:=4√x2+2x+10+ln|(x+1)+√(x+1)2+9|+C Final AnswerThus...
Evaluate the integral:∫0π4ln(2secx)dx. Question: Evaluate the integral:∫0π4ln(2secx)dx. Integral: Some important rules of integrals are as follows: 1.∫[f(x)+g(x)]dx=∫f(x)dx+∫g(x)dx 2.∫[f(x)−g(x)]dx=∫f(x)dx−∫g(x)dx ...
Evaluate: Integration dx / {5 + 2x^2} Evaluate: Integration of {6 x^{5 / 2} dx} Evaluate the indefinite integral. Integrate (ln (x)) / (x^4) dx Evaluate the indefinite integral of ((ln x)^30)/x dx. (Use C for the constant of integration.) ...
In order to express the results in a compact form, we introduce the notation a± for the integration weights w(a+, x) = 2a x2 − a2 w(a−, x) = 2x x2 − a2 (A.2) These weights are simply the linear combinations of the conventional weights w(a, x) = 1 x−a : w...