Strategy: Use Integration by Parts. Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math problems instantly.

\int \ln {x}\mathrm {d}x 为解决这一问题，直接使用分部积分公式即可，令： u = \ln {x},v = \mathrm {x} 进一步得到： \mathrm {d}u = \frac {1} {x}\mathrm {d}x, \mathrm {d}v = \mathrm {d}x 根据分部积分公式： \int u…

\lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx \sum_{n=0}^{\infty}\frac{3}{2^n} Show More

2018年5月8日 · 现在就是∫ln x dx 那就把v(x)当作ln x. u'(x)当作1， u(x)就等于x. ∫ln x dx=x × ln x －∫x×1/x dx＋c ＝xlnx－x +c

2 天之前 · 最近在研读小平邦彦先生所著的《微积分入门》一书，现摘录几例书中证明过的积分 \displaystyle 1.\large\begin{equation} \int_{0}^{1}\frac{\ln(1+x)}{1+x^{2}}\text dx \end{equation} 解 令 \displaystyle x=\t…

Strategy: Use Integration by Parts.

The Integral Calculator lets you calculate integrals and antiderivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. It helps you …

2023年11月14日 · $$= \int d(x\cdot\ln(\ln x)) - \int \frac{1}{\ln x}dx$$ $$ = x\cdot\ln(\ln x) + c - \int \frac{1}{\ln x}dx$$ The right hand side integral is also known as "logarithmic integral" and is denoted by $\operatorname{li}(x)$ .

One approach to evaluate the integral of \tfrac{2x}{2x+1} is to write it as: \eqalign{\int\dfrac{2x}{2x+1}\mathrm dx&=\int\dfrac{-1+(2x+1)}{2x+1}\mathrm dx\\&=\int\left[\dfrac{-1}{2x+1}+\dfrac{2x+1}{2x+1}\right]\mathrm dx\\ &=\int\left[\dfrac{-1}{2x+1}+1\right]\mathrm dx\\ &=\int\dfrac{-1}{2x+1}\mathrm dx+\int1\,\mathrm dx\\ &=\int-\dfrac{1}{2x ...

\int\ln(\sin x)dx 的计算. 由于 \ln(\sin x) 的 傅里叶级数 为 \color{purple}{\ln(\sin x)= -\ln2-\sum_{n=1}^\infty\frac{\cos2nx}{n}} \\ 所以 \int\ln(\sin x)dx= -\ln2\int dx-\int\sum_{n=1}^\infty\frac{\cos2nx}{n}dx= -x\ln2-\sum_{n=1}^\infty\frac{\sin2nx}{2n^2}+C \\ 那么