The antiderivative rules are common for types of functions such as trigonometric, exponential, logarithmic, and algebraic functions. Antiderivative Power Rule Now, the antiderivative rule of power of x is given by ∫xn dx = xn+1/(n + 1) + C, where n ≠ -1. This rule is commonly known...
Write ( 1/(x√(x^2-1))) as a function. ( f(x)=1/(x√(x^2-1))) The function( F(x)) can be found by finding the indefinite integral of the derivative( f(x)). ( F(x)=∫ f(x)dx) Set up the integral to solve. ( F(x)=∫ 1/(x√(x^2-1))dx) Rewrite...
The antiderivative of∫ 1(√(1-x^2))dxcan be either arcsin x+C or - arccos x+C. Does th
An antiderivative of f(x)=F(x) =int[log(logx)+(logx)^(-2)]dx+c =xlog(logx)-int(x)/(xlogx)dx+int(logx)^(-2)dx+c Integrating by parts in the first integral =xlog(logx)-[x(logx)^(-1)+int(logx)^(-2)dx]+int(logx)^(-2)dx+c [Again integrating by parts
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;
Example 1: 3x=7 log9x=3 Lesson Quiz Course 13Kviews What is a Natural Logarithm Definition? e ln(x)=y logex=y e exponential Properties of natural logs. Derivative of Natural Log dydx=ddxln(x). To find the derivative ofln(x), let's start with the following expre...
Compute the given initial conditions to get the value of constant of integration. Answer and Explanation:1 Simplifying the given differential equation, we have: {eq}dy=(5 x ^ { - 5 } + 2 x ^ { - 1 } - 1)d x {/eq} On integrating ...
Write 1−sin2(x)1-sin2(x) as a function. f(x)=1−sin2(x)f(x)=1-sin2(x)The function F(x)F(x) can be found by finding the indefinite integral of the derivative f(x)f(x). F(x)=∫f(x)dxF(x)=∫f(x)dxSet up the integral to solve. F(x)=∫1−sin2(x)dxF(x...
Answer to: Find the antiderivative, F(x), with F'(x) = f(x) and F(0) = 1. f(x) = -7 x. By signing up, you'll get thousands of step-by-step...
{eq}\displaystyle \int (2.5x^5-x-1.25)dx {/eq} Anti-Derivative of a Function: The anti-derivative is nothing but another name of the integration. It has a unique symbol {eq}\int , {/eq} called an integral. The general notation is: $$\int_a^b f(x) dx $$ Where {eq}f(...