An antiderivative of function f(x) is a function whose derivative is equal to f(x). Is integral the same as antiderivative? The set of all antiderivatives of a function is the indefinite integral of the function. The difference between any two functions in the set is a constant. ...
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...
What is the antiderivative of \frac{2(sin(2x))}{sin(x)}? What is the antiderivative of r(x) = -6e^{x + 6}? (Do not include the constant C in your answer.) What is the general antiderivative of \int \left(x^9 + 9^x\right)\,dx? (a) 9x^8 + \ln(9)9^x...
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}{x} dx ...
Properties of natural logs. Derivative of Natural Log dydx=ddxln(x). To find the derivative ofln(x), let's start with the following expression: y=ln(x) ey=x ddxey=ddxx ddxey=eydydx ddxx=1 eydydx=1 Solving fordydxgives us ...
( 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(1/2x^2(ln)(x)-1/4x^2)+C)反馈...
Consider the functionf(x)=x2−1x2+1,wherex∈R.At what value ofxdoesf(x)attain minimum value? What is the minimum value off(x)? View Solution Free Ncert Solutions English Medium NCERT Solutions NCERT Solutions for Class 12 English Medium ...
If f(x)=x3+2x, then find the value of f(3). View Solution The function f(x)=(3x−1)2sinx⋅ln(1+x),x≠0, is continuous at x=0, Then the value of f(0) is View Solution The function f(x)=(3x−1)2sinx⋅ln(1+x),x≠0, is continuous at x=0, Then the value ...
int 8e^{2x}+frac{1}{2^{5xdx Find the antiderivative. \int \dfrac{1}{(4x+1)^3}dx Find the antiderivative. \int \dfrac{dx}{x \ln x} Find the antiderivative: int x2 + 9 x3 - 9x dx Find the antiderivative: int x3 + 2x x - 1 dx Find the antiderivative. int 4^{9x}dx ...
Given that the antiderivative of f(x)=1x is F(x)=ln|x|+C, evaluate ∫121xdx. Definite Integration: Let function b is continous on [a,c]P is a differentiable function on (a,c) such that, ∀x∈(a,c),ddxP(x)=b(x) then, ∫acb(...