Evaluate ∫ln(1+x)dx. Integration by Parts:Integration by parts is an integration technique implemented to integrate a product of two functions. To apply integration by parts to evaluate an integral of a product, simply follow the formula given below: ...
解析 $$,解: \int1n(1+x)dx \\ =x \ln(1+x)- \int \frac{x}{1+x}dx \\ =x \ln(1+x)- \int \frac{1+x-1}{1+x}dx \\ =x \ln(1+x)- \int 1dx+ \int \frac{1}{1+x}dx \\ =x \ln(1+x)-x+1n(1+x)+c(c为代数 $$ 倍常数) ...
【解析】 $$ 2 \ln 2 - 1 $$ 结果一 题目 【题目】用Newton-Leibniz公式计算下列定积分∫_(-1)^1|x|dx 答案 【解析】∫_(-1)^1|x|dx=∫_(-1)^9-xdx+∫_0^1xdx=-1/2x^2|_(-1)^0+1/2x^2 或∫_(-1)^1|x|dx=2∫_0^1|x|dx=2∫_0^1xdx=x^2∫_0^1=1.(...
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...
∫ex2+lnxdx View Solution Evaluate: (i)∫(sin(logx)xdx(ii)∫emtan(−1)x1+x2dx View Solution Free Ncert Solutions English Medium NCERT Solutions NCERT Solutions for Class 12 English Medium NCERT Solutions for Class 11 English Medium
Find dy if y = 3 ln (4 + x^4). Find d/dx ln (1 + x). Find y' and y'' for y = ln x/(1 + ln x). Find the value of \ln 2^{1000} if \ln 2 = 0.69314. Evaluate int_1^infty ln x x^2 dx. Evaluate lim x ln x x ...
【解析】 解 由分部积分法,有 $$ \int _ { 1 } ^ { e } x \ln x d x = \int _ { 1 } ^ { e } \ln x d \frac { x ^ { 2 } } { 2 } = ( \frac { x ^ { 2 } } { 2 } \ln x ) | _ { 1 } ^ { e } - \int _ { 1 } ^ { e } \frac { x ...
解析 【解析】 $$,解: \int1n(1+x)dx \\ =x \ln(1+x)- \int \frac{x}{1+x}dx \\ =x \ln(1+x)- \int \frac{1+x-1}{1+x}dx \\ =x \ln(1+x)- \int 1dx+ \int \frac{1}{1+x}dx \\ =x \ln(1+x)-x+1n(1+x)+c $$ (c为任意常数) ...
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...
Solution 1:∫01ln(1+x)1+x2dx=∫0π4ln(1+tanx)dx=∫0π4ln(1+tan(...