What is the integral of {eq}\int x \ln x dx {/eq}?Integration by Parts:If {eq}f(x) {/eq} is a logarithmic function and {eq}g(x) {/eq} is an algebraic function then integration of {eq}f(x) \cdot g(x) {/eq} is given by ...
\\ = \frac { 1 } { 2 } x ^ { 2 } \ln x - \frac { 1 } { 2 } \int x d x = \frac { 1 } { 2 } x ^ { 2 } \ln x - \frac { 1 } { 4 } x ^ { 2 } + C . $$ 结果一 题目 求∫xlnxdx 答案 解∫xlnxdx=∫lnxd(x^2)/2=1/2x^2lnx-∫((x^2)/2)...
解析 【解析】 解 因为 $$ \frac { 1 } { x } $$dx凑微分为dlnx,故 $$ \int \frac { \ln x } { x } d x = \int \ln x d \ln x = \frac { 1 } { 2 } \ln ^ { 2 } x + C $$ 结果一 题目 35cm灬24cm 答案 【解析】|a| 结果二 题目 【题目】五、看图,补全单词...
$\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}}}{...
Answer to: Integrate. \\ \int x^3 \ln x dx By signing up, you'll get thousands of step-by-step solutions to your homework questions. You can also...
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 ...
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) ...
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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。
Answer to: Evaluate the integral. \int x \ln x dx By signing up, you'll get thousands of step-by-step solutions to your homework questions. You can...