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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(...
Evaluate the indefinite integral of sec x (tan x - sec x). Find the antiderivative of the following function. f(x) = secx Integrate: \int 7 \tan^2 \sec x dx Find the antiderivative. f(x) = x^6 - 1/7 * x^6 Find the antiderivative of f(t) = \frac{3}{...
To find the antiderivative of the function 3x√1−9x with respect to x, we can follow these steps: Step 1: Rewrite the expressionWe start with the integral:∫3x√1−9xdxNotice that 9x=(32)x=(3x)2. Therefore, we can rewrite the expression inside the square root:1−9x=1−(3x...
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 ...
\int \dfrac{dx}{x \ln x} Find the antiderivative. int 8e^{2x}+frac{1}{2^{5xdx Find the antiderivative. \int \dfrac{1}{(4x+1)^3}dx Find the antiderivative. \int \sqrt[4]{10w}dw Find the antiderivative of \frac{1}{x^2 - x + 1} , i.e., \...
∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx Answer and Explanation: Given integral function:∫[8e2x+125x]dx To find the antiderivative of the integral function: $$\beg... Learn more about this topic: Integration Problems in Calculus | Examples & Solutions ...
Since ( -1) is constant with respect to ( x), move ( -1) out of the integral. ( 2((ln)(|x|)+C)-∫ xdx+∫ √2dx) By the Power Rule, the integral of ( x) with respect to ( x) is ( 1/2x^2). ( 2((ln)(|x|)+C)-(1/2x^2+C)+∫ √2dx) Since ( √2)...
log9x=3 Lesson Quiz Course 12Kviews 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 expression: ...
Answer to: Find the antiderivative. f(x) = sec2(x) + 1 By signing up, you'll get thousands of step-by-step solutions to your homework...