du= \frac{1}{x}dx v= \frac{1}{2}x^{2} $$ 利用公式$$ \intuad_{u}dx=uv- \int _{u}du $$ 即$$ \int \times \ln xdx= \frac{1}{2}x^{2}\ln x- \int \frac{1}{2}x^{2}d(\ln x) $$ $$ = \frac{x^{2}}{2}\ln x- \frac{1}{2}\int x^{2}d(\ln x) ...
利用分部积分法,\( \int x \ln x dx \) 可以分解为 \( \ln x \cdot \frac{x^2}{2} - \int \frac{x^2}{2} dx \),其结果为 ___。相关知识点: 试题来源: 解析 答案:\( \ln x \cdot \frac{x^2}{2} - \frac{x^3}{6} + C \) 反馈 收藏...
Find integral \int\limits_1^{500} (13^x - 11^x)\mathrm{dx} + \int\limits_2^{500} (11^x - 13^x) \mathrm{dx} Find the integral of x^3 sin(1 + x^4) dx. Find the integral of x^3 ln x dx. Find: integral of ((y^3 - 1)/(y))^2 dy. Find the integral of (x +...
$\int x \ln x dx = $ A. \[\frac{{{x}^{2}}\,\ln{(x)}}{2}-\frac{{{x}^{2}}}{4}+C\] B. \[ -x^2 +C\] C. \[\frac{{{x}^{2}}\,\ln{(x)}}{4}-\frac{{{x}^{2}}}{4}+C\] D. \[\frac{{{x}^{2}}\,\ln{(x)}}{2}-\frac{{{x}^{2}}}{...
∫f(x)⋅g(x)dx=f(x)∫g(x)dx−∫[∫g(x)dxd(f(x))dx]dx. Answer and Explanation:1 We are given integral ∫xlnxdx Perform the indefinite integral using integration by parts: {eq}\begin{align} \implies \int x \ln... ...
【解析】 解 由分部积分法,有 $$ \int _ { 1 } ^ { e } x \ln x d x = \int _ { 1 } ^ { e } \ln x d \frac { x ^ { 2 } } { 2 } = ( \frac { x ^ { 2 } } { 2 } \ln x ) | _ { 1 } ^ { e } - \int _ { 1 } ^ { e } \frac { x ...
View Solution ∫x(logx)2dx View Solution ∫[logx−11+(logx)2]2dx = View Solution Exams IIT JEE NEET UP Board Bihar Board CBSE Free Textbook Solutions KC Sinha Solutions for Maths Cengage Solutions for Maths DC Pandey Solutions for Physics ...
int(dx)/(x ln x) 01:18 intlogx.dx 02:12 int(log(log x))/(x)dx 02:38 int(log(log x))/(x)dx) is 03:47 Evaluate: int(log(logx)/x\ dx 04:10 Evaluate: int(log(logx)/x\ dx 02:58 int (log x )/(x) dx 01:57 int x log x dx = 03:31 int x log x, dx 01:30...
解析 ∫ln x\,dx = xln x - x + C 本题使用分部积分法求解。令 u = ln x,dv = dx,则 du = 1/xdx,v = x。根据分部积分公式,原式可化为: ∫ln x\,dx = xln x - ∫ x⋅1/xdx = xln x - ∫ dx = xln x - x + C。 因此,∫ln x\,dx = xln x - x + C。
We obtain the calculation of the derivative of u and calculate v integrating dv. Answer and Explanation: {eq}\eqalign{ & {\text{Let's solve the following integral:}}\,\,\,\int {{x^3}\ln x} \,dx,{\text{ applying the formula of integration by parts:}} ......