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}}}{...
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 ...
∫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... ...
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) ...
令$u = \ln x$,则 $du = \frac{1}{x} dx$, 将这两个量带入积分式中,得到: $\int \frac{1}{u} du$。 对$\int \frac{1}{u} du$ 进行积分计算: $\int \frac{1}{u} du = \ln |u| + C = \ln |\ln x| + C$。 所以不定积分 $\int \frac{1}{x\ln x} dx = \...
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...
Integrate: {eq}\int x^n \ln x dx{/eq} Method of Integration by Parts: Integration by parts is a special method of integration that is very often useful when two integrable functions are multiplied together. If we suppose that {eq}f {/eq} and {eq}g {/eq} are two real valued fun...
What is inte^(e^(x))e^(x) dx equal to ? 01:12 What is intsin^(2)xdx+intcos^(2)xdx equal to ? 01:05 What is int(xcosx+sinx)dx equal to 02:07 What is int(dx)/(sqrt(4+x^(2))) equal to ? 01:08 What is inte^(lnx) dx equal to ? 01:04 What is int(dx)/(xl...