int frac{1}{x(log x)^2} , dx = | vedclass

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

Question

(B) To solve the integral $\int \frac{1}{x(\log x)^2} \, dx$,we use the method of substitution.Let $t = \log x$.Then,differentiating both sides with r

Vedclass · Accepted Answer

$-\frac{1}{\log x} + c$

Vedclass · Answer

(B) To solve the integral $\int \frac{1}{x(\log x)^2} \, dx$,we use the method of substitution.Let $t = \log x$.Then,differentiating both sides with respect to $x$,we get $\frac{dt}{dx} = \frac{1}{x}$,which implies $dt = \frac{1}{x} \, dx$.Substituting these into the integral,we get:$\int \frac{1}{t^2} \, dt = \int t^{-2} \, dt$.Using the power rule for integration $\int x^n \, dx = \frac{x^{n+1}}{n+1} + c$,we have:$\int t^{-2} \, dt = \frac{t^{-2+1}}{-2+1} + c = \frac{t^{-1}}{-1} + c = -\frac{1}{t} + c$.Finally,substituting $t = \log x$ back into the expression,we get:$-\frac{1}{\log x} + c$.

$\int \frac{1}{x(\log x)^2} \, dx = $

Similar Questions

$\int {\frac{t}{e^{3t^2}}} \, dt = $

If $\int \frac{2 \sin 2x - 3 \cos x}{2 \sin^2 x - 3 \sin x + 4} dx = f(x) + c$ where $c$ is the constant of integration, then $f\left(\frac{\pi}{2}\right) - f(0) =$

$\int \frac{dx}{(a^2 + x^2)^{3/2}}$ is equal to

Integrate the function: $\frac{1}{x \sqrt{ax - x^{2}}} \quad \left[ \text{Hint: } x = \frac{a}{t} \right]$

$\int x\sqrt{1 + x^2} \, dx = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module