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

Answer

$
\begin{aligned}
& \text { Let } I=\int e^x \frac{1+x}{(2+x)^2} d x \\
& =\int e^x\left[\frac{(2+x)-1}{(2+x)^2}\right] d x \\
& =\int e^x\left[\frac{1}{2+x}-\frac{1}{(2+x)^2}\right] d x
\end{aligned}
$
Let $f(x)=\frac{1}{2+x}$
$
\begin{aligned}
& \therefore f^{\prime}(x)=\frac{-1}{(2+x)^2} \\
& \therefore I=\int e^x[f(x)+f \prime(x)] d x \\
& =e^x \cdot f(x)+c \\
& =e^x \cdot \frac{1}{2+x}+c \\
& \therefore I=\frac{e^x}{2+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

Find the Price Index Number using the Simple Aggregate Method.
Use 1995 as the base year in the following problem.
COMMODITYPQRST
PRICE ( IN RS. ) IN 19951520242328
PRICE (IN RS.) IN 20002738324045
→
Construct the truth table for each of the following statement patterns : (~p ∨ q) ∧ (~p ∧ ~q)
→
A shopkeeper insures his shop and godown are valued at ₹ 5,00,000 and ₹ 10,00,000 respectively for 80% of their values. If the rate of premium is 8%, find the total annual premium.
→
Determine whether the following statement patterns is a tautology or a contradiction or a contingency:
[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~q)]
→
Find $\frac{d y}{d x}$ if, :
$
y=\left(5 x^3-4 x^2-8 x\right)^9
$
→
The income of the broker remains unchanged though the rate of commission is increased from $4\%$ to $5\%.$ Find the percentage reduction in the value of the business.
→
Evaluate the following definite integrals : $\int_1^3 \log x d x$
→
Calculate the cost of living index.
GroupBase YearBase YearCurrent Year
PriceQuantityPrice
Food13210170
Clothing15412160
Fuel & Lighting16420180
House Rent17518195
Miscellaneous1285120
→
Using the truth table, prove the following logical equivalences:
~p ∧ q ≡ (p ∨ q) ∧ ~p
→
A person takes a life policy for ₹ 2,00,000 for a period of 20 years. He pays premium for 10 years during which bonus was declared at an average rate of ₹ 20 per year per thousand. Find the paid up value of the policy if he discontinuous paying premium after 10 years.
→