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...
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. ...
1. Find the antiderivative of f(x) = x^2 + cos x . 2. Evaluate \lmoustache \sqrt{1-x^3} \ x^2 dx. Find the antiderivative of the function f(x) = tan^2(x) + (2x - 3)^5. Find an antiderivative for the function f(x) = \dfrac{1...
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 ...
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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 ...
sec(x)tan(x)? Show all the steps. Antiderivative:In calculus, the term antiderivative denotes indefinite integration since the differentiation and integration are opposed to each other. It is also called antidifferentiation or inverse derivative, which means the inverse of derivative (i...
What is the general antiderivative of \int \left(x^9 + 9^x\right)\,dx? (a) 9x^8 + \ln(9)9^x + C (b) 9x^{10} + \ln(9)9^x + C (c) \frac{1}{10}x^{10} + \frac{1}{\ln(9)}9^x + C (d) \frac{1}{10}x^{10} + 9^x + C What is the ant...
1) Find the area of the region bounded by the given curves. y = xe^{-0.2x}, y = 0, x = 1. 2) Find the area of the region bounded by the given curves. y = 5 \ln x, y = x \ln x Find the...