\\ = \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 . $$ 结果一 题目 求∫xlnxdx 答案 解∫xlnxdx=∫lnxd(x^2)/2=1/2x^2lnx-∫((x^2)/2)...
Answer to: Evaluate the integral. \int x \ln x dx By signing up, you'll get thousands of step-by-step solutions to your homework questions. You can...
What is the integral of {eq}\int x \ln x dx {/eq}?Integration by Parts:If {eq}f(x) {/eq} is a logarithmic function and {eq}g(x) {/eq} is an algebraic function then integration of {eq}f(x) \cdot g(x) {/eq} is given by ...
du= \frac{1}{x}dx v= \frac{1}{2}x^{2} $$ 利用公式$$ \intuad_{u}dx=uv- \int _{u}du $$ 即$$ \int \times \ln xdx= \frac{1}{2}x^{2}\ln x- \int \frac{1}{2}x^{2}d(\ln x) $$ $$ = \frac{x^{2}}{2}\ln x- \frac{1}{2}\int x^{2}d(\ln x...
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解:由定积分分部积分公式 $$ \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 ^ { 2 } } { ...
Answer to: Find the following integral: \int \frac{\ln (x)}{\sqrt x} dx By signing up, you'll get thousands of step-by-step solutions to your...
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。
int(xlnx)/((x^2-1)^(3/2))dx 04:33 int(e^(x))/((1+x)^(3))dx-int(e^(x))/(2(1+x)^(2))dx= 02:16 (i) \ int \ (x^3-1)/(x^2) \ dx quad (ii)int \ (x^(2//3)+1)dx 01:29 int(xlnx)/(x^(2)-1)^(3//2) dx equals 05:24 निमिन्...