Write an anti-derivative for the following fu | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) We know that the derivative of $\log x$ with respect to $x$ is $\frac{1}{x}$ for $x > 0$. Also,for $x < 0$,let $y = -x$,then $\frac{d}{dx}(\log(-x

Vedclass · Accepted Answer

$\log |x|$

Vedclass · Answer

(A) We know that the derivative of $\log x$ with respect to $x$ is $\frac{1}{x}$ for $x > 0$. Also,for $x Combining these two cases,we get $\frac{d}{dx}(\log |x|) = \frac{1}{x}$ for all $x 
eq 0$. By the definition of an anti-derivative,if $\frac{d}{dx}(F(x)) = f(x)$,then $F(x)$ is an anti-derivative of $f(x)$. Therefore,$\log |x|$ is an anti-derivative of $\frac{1}{x}$.

Write an anti-derivative for the following function using the method of inspection: $\frac{1}{x}, x \neq 0$

Similar Questions

$\int {{x^x}(1 + \log x)\,dx} $ is equal to

If $f(x) = \frac{3-8x}{3x-1}$ and $\int f(y) dy = Ay + B \log |3y-1| + C$, then $\frac{A-3B}{2} =$

$\int \frac{dx}{\sin x + \cos x} = $

$\int \frac{\cos x+x \sin x}{x(x+\cos x)} d x=$

If $\int [ \cos(x) \cdot \frac{d}{dx}(\csc(x)) ] dx = f(x) + g(x) + c$,then $f(x) \cdot g(x) =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module