Evalute the following integrals: 1 x dx - Vidyadip

Question

Evalute the following integrals:
$\int\frac{1}{\text{x}\log\text{x}}\text{dx}$

✓

Answer

Here, we are considering $\log\text{x}$ as $\log_\text{e}\text{x}$.
Let $\text{I}=\int\frac{1}{\text{x}\log\text{x}}\text{dx}$
Putting $\log\text{x}=\text{t}$
$\Rightarrow\frac{1}{\text{x}}=\frac{\text{dt}}{\text{dx}}$
$\Rightarrow\frac{1}{\text{x}}\text{dx}=\text{dt}$
$\therefore\text{I}=\int\frac{1}{\text{t}}\text{dt}$
$=\log|\log\text{x}|+\text{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Given $X \sim B (n, p)$. If $E ( X )=6$, and $\operatorname{Var}( X )=4.2$, find the value of $n$ and $p$.

The binary operation *: R × R → R is defined as a * b = 2a + b. Find (2 * 3) * 4.

Evaluate the following:

$\int \frac{t \cdot \sin ^{-1} t}{\sqrt{1-t^2}} d t$

If $\bar{a}=3 \hat{i}-2 \hat{j}+7 \hat{k}, \bar{b}=5 \hat{i}+\hat{j}-2 \hat{k}$ and $\bar{c}=\hat{i}+\hat{j}-\hat{k}$ then find $\bar{a} \cdot(\bar{b} \times \bar{c})$

What is the value of the determinant $\begin{vmatrix}0&2&0\\2&3&4\\4&5&6\end{vmatrix}?$

Integrate the following functions w.r.t. x:

$\frac{\sqrt{\tan x}}{\sin x \cdot \cos x}$

$\sin^{-1}\frac{1}{2}-2\sin^{-1}\frac{1}{\sqrt2}$

Evaluate the following determinant:
$\begin{vmatrix}\text{x}&-7\\\text{x}&5\text{x}+1 \end{vmatrix}$

Three shopkeepers A, B and C go to a store to buy stationary. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. Cpurchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook costs 40 paise, a pen costs Rs. 1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual's bill.

Find the general solution of $\cos x+\sin x=1$.