Question
Evaluate: $\int \frac{1}{x \log x \log (\log x)} d x$
✓
Answer
Let $I=\int \frac{1}{x \cdot \log x \log (\log x)} d x$
Put log (log x) = t
Differentiating w.r.t. x, we get
$\frac{1}{\log x} \frac{.1}{x} d x=d t$
$I=\int \frac{1}{t} d t=\log |t|+c$
$I=\log |\log (\log x)|+c$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Differentiate the following w. r. t. x.$\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$
→Find the principal values of the following:
$\tan^{-1}\Big(2\cos\frac{2\pi}{3}\Big)$
→$\tan^{-1}\Big(2\cos\frac{2\pi}{3}\Big)$
Find the distance of the point $\mathrm{P}(0,2,3)$ from the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$.
→
Show that $\bar{a} \times(\bar{b} \times \bar{c})+\bar{b} \times(\bar{c} \times \bar{a})+\bar{c} \times(\bar{a} \times \bar{b})=0$
→Using truth tables prove the following logical equivalences. (p ∨ q ) → r ≡ (p → r) ∧ (q → r)
If $y=\sin ^{-1}(3 x)+\sec ^{-1}\left(\frac{1}{3 x}\right)$, find $\frac{d y}{d x}$
→vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are such that $|\vec{\text{a}}|=\sqrt{3},\big|\vec{\text{b}}\big|=\frac{2}{3}$ and $\big(\vec{\text{a}}\times\vec{\text{b}}\big)$ is a unit vector. write the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$
→Find the approximate value of given functions, at required points.
→$(3.97)^4$
Using truth tables prove the following logical equivalences. p → (q ∧ r) ≡ (p → q) ∧ (p → r)
Evaluate the following definite integrals:$\int_{0}^\limits{\frac{\pi}{2}}\text{x}\cos\text{x}\text{ dx}$
→