\int (x+1)^2dx=\int x^2+2x+1dx=\frac{1}{3}x^3+x^2+x+C 法二:换元法令t=x+1 , \frac{dt}{dx}=1\Rightarrow dt=dx,把所有的 x 都用t 来代替,于是 \int (x+1)^2dx=\int t^2 dt=\frac{1}{3}t^3=\frac{1}{3}(x+1)^3+C。 我们可以发现通过代换这样积分就简单了很多...
{eq}\displaystyle \int_1^e \dfrac {\ln^2 x + 1} {x}\ dx {/eq}. Integrals: Anti-derivatives and integral refer to the process of operating on a function such that we find out what result function has a derivative that has the form of our original function. Integrals are...
View Solution The value of the integral∫∞0xlogx(1+x2)2dxis View Solution View Solution Free Ncert Solutions English Medium NCERT Solutions NCERT Solutions for Class 12 English Medium NCERT Solutions for Class 11 English Medium NCERT Solutions for Class 10 English Medium ...
∫(2x−1)ln(6x)dx Question:Evaluate the integral: ∫(2x−1)ln(6x)dx Evaluate the Integral:The integral of a function is related to the antiderivative of a function. We will be discussed these concepts in the Fundamental Theorem of Calculus. The integral will have applications to...
∫02|2x−1|dxSplitting an Absolute Value Integral into Two PartsIn order to integrate a function involving absolute value, we first must determine where the function inside the absolute value is positive or negative. Then we split the integral into two separate integrals based on that...
( (ln)(x)dx) 相关知识点: 试题来源: 解析 Since ( d) is constant with respect to ( x), move ( d) out of the integral.( d∫ (ln)(x)xdx)Integrate by parts using the formula( ∫ udv=uv-∫ vdu), where ( u=(ln)(x)) and ( dv=x).( d((ln)(x)(1/2x^2)-∫ 1/2x^...
I would like to know how to evaluate the integral $$\int^1_0\frac{\ln{x} \ \mathrm{Li}_2(x)}{1-x}dx$$ I tried expanding the integrand as a series but made little progress as I do not know how to evaluate the resulting sum. \begin{align} \int^1_0\frac{\ln{x} \ \math...
Ahmed's Integral∫01tan−1(x2+2)(x2+2)(x2+1)dx 方法一: 令I=∫01tan−1(2+x2)(1+x2)2+x2dx 及 f(t)=∫01tan−1(t2+x2)(1+x2)2+x2dx 其中f(1)=I. ⇒f′(t)=∫01dx(1+x2)2+x2ddttan−1(t2+x2)=∫01dx(1+x2)2+x22+x21+(t2+x2)2=...
The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan... 04:05 Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ... 06:57 Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2+1...
百度试题 结果1 题目In Exercises 1-20, find the integral.∫(x^3)/(x^2+1)dx dx 相关知识点: 试题来源: 解析 1/2x^2-1/2ln(x^2+1)+C 反馈 收藏