Write a value of _ex dx - Vidyadip

Question

Write a value of $\int\log_\text{e}\text{x}\text{ dx}$

✓

Answer

$\int\log_\text{e}\text{x}\text{ dx}$
$=\int1\cdot\log_\text{e}\text{x dx}$
$=\log_\text{e}\text{x}\int1\text{ dx}-\int\Big\{\frac{\text{d}}{\text{dx}}(\log_\text{e}\text{x})\int1\text{dx}\Big\}\text{dx}$
$=\log_\text{e}\text{x}\int1\cdot\text{dx}-\int\frac{1}{\text{x}}\cdot\text{x dx}$
$=\log_\text{e}\text{x}\cdot\text{x}-\int\text{dx}$
$=\text{x}\log_\text{e}\text{x}-\text{x}+\text{C}$
$=\text{x}(\log_\text{e}\text{x}-1)+\text{C}$

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.(3 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

Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
$\text{f}(\text{x})=\frac{1}{\text{x}^{2}+2}$

Find the equation of the line passing through the points (2, 1, 3) and perpendicular to the lines $\frac{\text{x}-1}{1}=\frac{\text{y}-2}{2}=\frac{\text{z}-3}{3}$ and $\frac{\text{x}}{-3}=\frac{\text{y}}{2}=\frac{\text{z}}{5}$

Differentiate the following w. r. t. x.$\tan ^{-1}\left(\frac{7 x}{1-12 x^2}\right)$

Show that the following equations represent a pair of lines. Find the acute angle between them : $(x-3)^2+(x-3)(y-4)-2(y-4)^2=0$

The probability distribution of a random variable $X$, the number of defects per 10 meters of a fabric is given by

$x$	0	1	2	3	4
$P ( X =x)$	0.45	0.35	0.15	0.03	0.02

Find the variance of $X$.

Solve the following differential equation
$5\frac{\text{dy}}{\text{dx}}=\text{e}^\text{x}\text{y}^4$

ABCD is a parallelogram and P is the point of intersection of its diagonals. If O is the origin of reference, show that $\overrightarrow{\text{OA}}+\overrightarrow{\text{OB}}+\overrightarrow{\text{OC}}+\overrightarrow{\text{OD}}=4\ \overrightarrow{\text{OP}}$.

Evaluate the following integrals:$\int\frac{\log\text{x}}{\text{x}^{\text{n}}}\text{dx}$

A particle moves along the curve $6 y=x^3+2$. Find the points on the curve at which $y$ -

coordinate is changing 8 times as fast as the x-coordinate.

State the converse, inverse and contrapositive of the conditional statement : 'If a sequence is bounded, then it is convergent'.