Evalute : 1 2 x+3 x x d x - Vidyadip

Question

Evalute : $\int \frac{1}{2 x+3 x \log x} d x$

✓

Answer

$
\text { Let } \begin{aligned}
I & =\int \frac{1}{2 x+3 x \log x} d x \\
& =\int \frac{1}{(2+3 \log x)} \cdot \frac{1}{x} d x
\end{aligned}
$
Put $2+3 \log x=t \quad \therefore \frac{3}{x} d x=d t$
$\therefore \frac{1}{x} d x=\frac{d t}{3}$
$
\begin{aligned}
\therefore I & =\int \frac{1}{t} \cdot \frac{d t}{3}=\frac{1}{3} \int \frac{1}{t} d t \\
& =\frac{1}{3} \log |t|+c \\
& =\frac{1}{3} \log |2+3 \log x|+c .
\end{aligned}
$

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 Integration (p-1)→Integration (p-1) — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

An inquiry of 50 families to study the relationship between expenditure on accommodation (₹ x) and expenditure on food and entertainment ₹ gave the following result:
$
\Sigma x=8500, \Sigma y=9600, \sigma_x=60, \sigma_y=20, r=0.6
$
Estimate the expenditure on food and entertainment when expenditure on accommodation is ₹ 200

Find $\frac{d^2 y}{d x^2}$, if $y = x ^2 \cdot e ^{ x }$

If $A=\left[\begin{array}{cc}1 & -2 \\ 5 & 3\end{array}\right], B=\left[\begin{array}{cc}1 & -3 \\ 4 & -7\end{array}\right]$, then find the matrix $A-2 B+6 I$, where $I$ is the unit matrix of order 2 .

Using the truth table, prove the following logical equivalences:
[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r

Evalute : $\int e^x \frac{1+x}{(2+x)^2} d x$

Find $\frac{d y}{d x}$ if, :
$
x=2 a t^2, y=a t^4
$

Find the differential equation whose general solution is $x^3+y^3=$ 35ax.

A stock worth ₹ 7,00,000 was insured for ₹ 4,50,000. Fire burnt stock worth ₹ 3,00,000 completely and damaged there remaining stock to the extent of 75% of its value. What amount can be claimed undertaken policy?

A factory building is insured for $\left(\frac{5}{6}\right)^{\text {th }}$ of its value at a rate of premium of $2.50 \%$. If the agent is paid a commission of ₹ $2,812.50$, which is $7.5 \%$ of the premium, find the value of the building.

$\int_2^3 \frac{x}{x^2-1} d x$