Find the indefinite integral, ∫1xlnx2dx. (Remember to useln(|u|) where appropriate. Integral: U-Substitution: The integrand involves a log term in the denominator. We can simplify this integral by a substitution. if we choose this log term as a ne...
( (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^...
The integration of the single functionln(f(x))is usually evaluate by using the formula of the integration by parts, which is given as∫uvdx=u∫vdx−∫(dudx∫vdx)dx, where u and vare functions of x. For solving the integration ofln(f(x)), we takeln...
p=1 时, \int \frac{1}{x}\ dx=\ln x+C, y=\ln x 是没有上界的,因此级数 1+\frac{1}{2}+\frac{1}{3}+\cdots 发散 p\ge 1 时,\int_1^\infty \frac{1}{x^p}\ dx=\int_1^\infty x^{-p} \ dx=\frac{x^{-p+1}}{-p+1}\bigg]^\infty_1=\frac{1}{p-1}. 因此当...
(2) \int xe^x dx \int x e^{x} d x=\int x d e^{x}=x e^{x}-\int e^{x} d x=x e^{x}-e^{x}+c . (3) \int x \ln xdx \int x \ln x d x=\int \ln x d\left(\frac{1}{2} x^{2}\right)=(\ln x)\left(\frac{1}{2} x^{2}\right)-\int \frac{1...
716ζ(3)ln2−18π2ln22 which can be found in another MSE post. To evaluate the integral in the first part, integrating by parts give ∫π/20cotx(cos2nx−14n2+xsin2nx2n)dx=I1(n)4n2+I2(n)2n It's obvious that I1(0)=0, I1(n)−I1(n−1)=∫π/20−2cotxsinx...
-\int_{0}^{1}{\frac{\ln^s{(x)}}{-x}\ln{(1-xy)}\Big|_{0}^{1}}dx \\ &= -\int_{0}^{1}{\ln^s{(x)}\frac{\ln{(1-x)}}{x}}dx \end{align} $$ need to know that $$ \text{Li}_2{(x)}=-\int_{0}^{x}{\frac{\ln{(1-t)}}{t}}dt ...
The given integral is {eq}\displaystyle \int\limits_1^e x {(\ln x)^2}dx {/eq}. Integrating by parts, we get {eq}\displaystyle...Become a member and unlock all Study Answers Try it risk-free for 30 days Try it risk-free Ask a question Our experts can answer your tough ...
百度试题 结果1 题目Calculate the integral:∫_2^(+∞)(dx)(x^2-1)Which answer is CORRECT?12ln 3ln 31212ln x 相关知识点: 试题来源: 解析 A 反馈 收藏
The value of the integral int (e ^(-1))^(e ^(2))|(ln x )/(x)|dx is: 04:20 int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1... 05:46 If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then...