Download App

Integration (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Integration (p-1)2 Marks
Question
Evalute : $\int e^x \frac{x}{(x+1)^2} d x$
✓

Answer

$
\begin{aligned}
LetI & =\int e^x \cdot \frac{x}{(x+1)^2} d x \\
& =\int e^x\left[\frac{(x+1)-1}{(x+1)^2}\right] d x \\
& =\int e^x\left[\frac{1}{x+1}-\frac{1}{(x+1)^2}\right] d x
\end{aligned}
$
Put $f(x)=\frac{1}{x+1}$
Then $f^{\prime}(x)=\frac{d}{d x}(x+1)^{-1}=-1(x+1)^{-2} \cdot \frac{d}{d x}(x+1)$
$
\begin{aligned}
& =\frac{-1}{(x+1)^2} \times(1+0)=\frac{-1}{(x+1)^2} \\
\therefore I=\int e^x[ & \left.f(x)+f^{\prime}(x)\right] d x \\
& =e^x \cdot f(x)+c=e^x \cdot \frac{1}{x+1}+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

Find the Price Index Number using the Simple Aggregate Method.
Use 2000 as the base year in the following problem.
CommodityPrice (in Rs.) for year 2000Price (in Rs.) for year 2006
Watch9001475
Shoes18002300
Sunglasses6001040
Mobile45008500
→
A salesman gets a commission of 6.5% on the total sales made by him and a bonus of 1% on sales over $\text{₹}$ 50,000. Find his total income on a turnover of $\text{₹}$ 75,000.
→
Find the Price Index Number using the Simple Aggregate Method.
Use 1990 as the base year in the following problem.
CommodityUnitPrice (in Rs.) for 1990Price
(in Rs.) for 1997
Butterkg2133
Cheesekg3036
Milklitre2529
Breadloaf1014
Eggsdoz2436
Gheetin250320
→
Find $\frac{d y}{d x}$ if, :
$
y=\left(5 x^3-4 x^2-8 x\right)^9
$
→
Evalute : $\int e^x \frac{1+x}{(2+x)^2} d x$
→
If $A =\left[\begin{array}{ccc}1 & 2 & -5 \\ 2 & -3 & 4 \\ -5 & 4 & 9\end{array}\right]$, prove that $A ^{\top}= A$.
→
Find the Price Index Number using the Simple Aggregate Method.
Assume 2000 to be a base year in the following problem.
FruitUnitPrice (in Rs.) in 2000Price (in Rs.) in 2007
Mangodoz250300
Bananadoz1224
Applekg80110
Peachkg7590
Orangedoz3365
Sweet Limedoz3045
→
For each of the following matrices, find its transpose and state whether it is symmetric, skew-symmetric or neither:
$\left[\begin{array}{ccc}2 & 5 & 1 \\ -5 & 4 & 6 \\ -1 & -6 & 3\end{array}\right]$
→
If $A=\left[\begin{array}{cc}5 & -3 \\ 4 & -3 \\ -2 & 1\end{array}\right]$, prove that $\left(A^{\top}\right)^{\top}=A$.
→
Find the mean of the number of heads in three tosses of a fair coin.
→