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 ...
The antiderivative of1sin2x+tan2xis View Solution Free Ncert Solutions English Medium NCERT Solutions NCERT Solutions for Class 12 English Medium NCERT Solutions for Class 11 English Medium NCERT Solutions for Class 10 English Medium NCERT Solutions for Class 9 English Medium ...
Find the antiderivative of: 1) \int {\sin x}{(\cos x- \cos x \sin^2x)} \, dx 2) \int \cos^2x(1+\sin^2x) \, dx Find the antiderivative of F(x) = \dfrac{x^2 +3x^3 -x^4}{x^5}. Find the antiderivative. f(x) = x 1/3/x 2/3 Find the antid...
Given function: f(x)=sec2(x)+1 We want to find the antiderivative of the function: $$\begin{a...Become a member and unlock all Study Answers Start today. Try it now Create an account Ask a question Our experts can answer your tough homework and study questions. Ask a ...
The integral ∫1√1−t2dt is a standard integral that evaluates to:sin−1(t)+CThus, we have:1ln(3)(sin−1(t)+C)=1ln(3)sin−1(3x)+C Step 5: Final expressionTherefore, the antiderivative of the original function is:∫3x√1−9xdx=1ln(3)sin−1(3x)+C ConclusionThe ...
Properties of natural logs. Derivative of Natural Log dydx=ddxln(x). To find the derivative ofln(x), let's start with the following expression: y=ln(x) ey=x ddxey=ddxx ddxey=eydydx ddxx=1 eydydx=1 Solving fordydxgives us ...
( d(((ln)(x)x^2)/2-1/2(1/2x^2+C))) Simplify the answer. ( d(1/2x^2(ln)(x)-1/4x^2)+C) The answer is the antiderivative of the function( f(x)=(ln)(x)dx). ( F(x)=)( d(1/2x^2(ln)(x)-1/4x^2)+C)反馈...
Since ( -1) is constant with respect to ( x), move ( -1) out of the integral. ( 2((ln)(|x|)+C)-∫ xdx+∫ √2dx) By the Power Rule, the integral of ( x) with respect to ( x) is ( 1/2x^2). ( 2((ln)(|x|)+C)-(1/2x^2+C)+∫ √2dx) Since ( √2)...
int frac{1}{sqrt{9xdx Find the antiderivative. \int \dfrac{dx}{x \ln x} Find the antiderivative. int 8e^{2x}+frac{1}{2^{5xdx Find the antiderivative. \int \dfrac{1}{(4x+1)^3}dx Find the antiderivative. \int \sqrt[4]{10w}dw Find the antiderivative...
∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx Answer and Explanation: Given integral function:∫[8e2x+125x]dx To find the antiderivative of the integral function: $$\beg... Learn more about this topic: Integration Problems in Calculus | Examples & Solutions ...