Question
Evaluate:$\int\text{x log 2x dx}$.
✓
Answer
$\text{I}=\int\log2\text{x}\cdot\text{x dx}=\log2\text{x}\cdot\frac{\text{x}^{2}}{2}-\int\frac{1}{\text{x}}\cdot\frac{\text{x}^{2}}{2}\text{dx}+\text{c}_{1}$= $\frac{\text{x}^{2}}{2}\cdot\log\text{2x}-\frac{1}{2}\int\text{x dx + c}_{1}=\frac{\text{x}^{2}}{2}\cdot\log\text{ 2x}-\frac{\text{x}^{2}}{4}+\text{c}.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Evaluate the following integrals:
$\int\sin^3\text{x}\cos^5\text{x}\text{ dx}$
→$\int\sin^3\text{x}\cos^5\text{x}\text{ dx}$
A bill for Rs. 7650 was drawn on 8th March 2005 at 7 months. It was discounted on 18 May 2005 and the holder of the bill received Rs. 7497. What rate of interest did the banker charge?
Find the rate of change of the volume of a ball with respect to its radius r. How fast is the volume changing with respect to the radius when the radius is 2cm?
If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.
Solve the following equation for x:
$\tan^{-1}(\text{x}+2)+\tan^{-1}(\text{x}-2)=\tan^{-1}\Big(\frac{8}{79}\Big),\text{x}>0$
→$\tan^{-1}(\text{x}+2)+\tan^{-1}(\text{x}-2)=\tan^{-1}\Big(\frac{8}{79}\Big),\text{x}>0$
Write the following in the simplest form:
$\tan^{-1}\Big\{\frac{\sqrt{1+\text{x}^2}+1}{\text{x}}\Big\},\text{x}\neq0$
→$\tan^{-1}\Big\{\frac{\sqrt{1+\text{x}^2}+1}{\text{x}}\Big\},\text{x}\neq0$
In a legislative assembly election, a political group hired a public relations firm to promote its candidate in three ways: telephone, house calls, and letters. The cost per contact (in paise) is given in matrix A as
The number of contacts of each type made in two cities X and Y is given by
Find the total amount spent by the group in the two cities X and Y.
The number of contacts of each type made in two cities X and Y is given by
Find the total amount spent by the group in the two cities X and Y.
In roulette, Figure, the wheel has 13 numbers 0, 1, 2,...., 12 maked on equally spaced slots. A player sets Rs 10 on a given number. He recieves Rs 100 from the organiser of the game if the ball comes to rest in this slot; otherwise he gets nothing. If X denotes the players net gain/loss, Find E(X).
If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are three unit vectors such that $\vec{\text{a}}\times\vec{\text{b}}=\vec{\text{c}},\vec{\text{b}}\times\vec{\text{c}}=\vec{\text{a}},\vec{\text{c}}\times\vec{\text{a}}=\vec{\text{b}}.$Show that $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ from an orthonormal right handed triad of unit vectors.
→If $\text{x}=4\text{z}^2+5,\text{y}=6\text{z}^2+7\text{z}+3$find $\frac{\text{d}^2\text{y}}{\text{dx}^2}.$
→