Download App

Question Bank [2022] — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Question Bank [2022]4 Marks
Question
$\int e ^x \frac{x}{(x+1)^2} d x$
✓

Answer

$\text { Let } I =\int e ^x\left(\frac{x}{(x+1)^2}\right) d x$
$=\int e ^x\left(\frac{(x+1)-1}{(x+1)^2}\right) d x$
$=\int e ^x\left(\frac{x+1}{(x+1)^2}-\frac{1}{(x+1)^2}\right) d x$
$=\int e ^x\left(\frac{1}{x+1}-\frac{1}{(x+1)^2}\right) d x$
$\text { Put } f ( x )=\frac{1}{x+1}$
$\therefore f ^{\prime}( x )=\frac{-1}{(x+1)^2}$
$\therefore \text { I }=\int e ^x\left[ f (x)+ f ^{\prime}(x)\right] d x$
$= e ^x \cdot f (x)+ c$
$\therefore I = e ^x\left(\frac{1}{x+1}\right)+ 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.(4 Marks)" from Question Bank [2022]→Question Bank [2022] — 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

Examine the function $f$ for maxima and minima, where $f(x)=x^3-9 x^2$+24 x
→
The probability distribution of a discrete r.v.X is as follows.
x 1 2 3 4 5 6
P(X = x) k 2k 3k 4k 5k 6k
Complete the following activity.
Solution: Since $\sum p_i=1$
$P(X \geq 3)=\square-\square-\square=\square$
→
A bill was drawn on 14th April 2005 for $\text{₹}$ 3,500 and was discounted on 6th July 2005 at 5% per annum. The banker paid $\text{₹}$ 3,465 for the bill. Find the period of the bill.
→
Evalute : $\int \frac{x^2+x-1}{x^2+x-6} d x$
→
Complete the table using 4 yearly moving average method.
YearProduction4 yearly
moving
total		4 yearly
centered
total		4 yearly centered
moving average
(trend values)
200619 ––
$\square$
200720 –$\square$
72
200817 14217.75
70
200916 $\square$17
$\square$
201017 133$\square$
67
201116 $\square$$\square$
$\square$
201218 14017.5
72
201317 14718.375
75
201421 ––
–
201519 ––
→
Find the area of the circle $x^2 + y^2 = 16$
→
Evalute : $\int \frac{5 x^2-6 x+3}{2 x-3} d x$
→
Given $P _{01}( M - E )=120, \sum p _1 q _1=300, \sum p _0 q _0=120, \sum p _0 q _1=320$, Find $P _{01}( L )$
→
A company manufactures 2 types of goods P and Q that requires copper and brass. Each unit of type P requires 2 grams of brass and 1 gram of copper while one unit of type Q requires 1 gram of brass and 2 grams of copper. The company has only 90 grams of brass and 80 grams of copper. Each unit of types P and Q brings profit of ₹ 400 and ₹ 500 respectively. Find the number of units of each type the company should produce to maximize its profit
→
Prove that the following pairs of statement patterns are equivalent:
(i) p ∨ (q ∧ r) and (p ∨ q) ∧ (p ∨ r)
(ii) p ↔ q and (p → q) ∧ (q → p)
(iii) p → q and ~q → ~p and ~p ∨ q
(iv) ~(p ∧ q) and ~p ∨ ~q
→