For example, we need to find the antiderivative of x ln x. Then, according to the sequence above, the first function is ln x and the second function is x. Therefore, we have ∫x ln x dx = ln x ∫x dx - ∫[(ln x)' ∫x dx] dx = (x2/2) ln x - ∫(1/x)(x2/2) dx...
Verify that F(x)=xln(x)−x is an antiderivative of ln(x). Proof of Anti-Derivative and By Parts Method: To prove the value of the anti-derivative of an integrand, we can apply the by parts method using the ILATE (inverse, logarithmic, algebraic, trigonometric, exp...
By the Power Rule, the integral of ( x) with respect to ( x) is ( 1/2x^2). ( d(((ln)(x)x^2)/2-1/2(1/2x^2+C))) Simplify the answer. ( d(1/2x^2(ln)(x)-1/4x^2)+C) The answer is the antiderivative of the function( f(x)=(ln)(x)dx). ( F(x)=)( d(...
unique property that ln(e^x) = x and e^(ln(x)) = x. The natural log "undoes" the exponential and vice versa. Natural logs follow the same properties of addition, subtraction, multiplication, and division as common logs since a natural log is nothing more than a common log of base ...
An antiderivative of a function f(x) is a function whose derivative is equal to f(x). ... An indefinite integral is an integral written without terminals;
∫143x2 dx, F(x)=x3+2 Anti-Differentiation: The process of finding a function f(x), given its derivative f'(x), is called anti-differentiation (or integration). If F'(x) = f(x), we say F(x) is an anti-derivative of f(x). For checking the...
1/x dx ln |x| + C E^x e^x + C a^x a^x/ln(a) + C Sin x -cos x Cos x Sin sec^2x Tan x sec x tan x sec x + C 1dx/1+x^2 Tan^-1 1/sqrt(1-x^2) sin^-1(x) 最好的學習方式。免費註冊。 註冊代表你接受Quizlet的服務條款和隱私政策 ...
Integrate: \frac {(x^2+1)}{((x-3)(x-2)^2)} dx What is the antiderivative of \frac{3x}{x^2}? Find the most general antiderivative. \int ( \frac { 8 } { \sqrt { 1 - x ^ { 2 } } } - \frac { 5 } { x } ) d x Find the indefinite integral.\int \frac{ \ln5x...
运算法则公式如下:1.lnx+ lny=lnxy2.lnx-lny=ln(x/y)3.lnxⁿ=nlnx4.ln(ⁿ√x)=lnx/n5.lne=16.ln1=0拓展内容:对数运算法则(rule of logarithmic operations)一种特殊的运算方法.指积、商、幂、方根的对数的运算法则。在数学中,对数是对求幂的逆运算,正如除法是乘法的倒数,反之亦然。 这意味着一...
1/x dx ln |x| + C E^x e^x + C a^x a^x/ln(a) + C Sin x -cos x Cos x Sin sec^2x Tan x sec x tan x sec x + C 1dx/1+x^2 Tan^-1 1/sqrt(1-x^2) sin^-1(x) 最好的學習方式。免費註冊。 註冊代表你接受Quizlet的服務條款和隱私政策 以Google帳戶繼續 關於...