allery$\int \dfrac{dx}{(x+1)(x+2)}$ equals
A$\log\left|\dfrac{x+2}{x+1}\right|+C$
B$\log\left|\dfrac{x+1}{x+2}\right|+C$
C$\log|(x+1)(x+2)|+C$
D$\dfrac{1}{(x+1)(x+2)}+C$
Answer & Solution
Correct answer: B. $\log\left|\dfrac{x+1}{x+2}\right|+C$
1. Partial fractions: $\dfrac{1}{(x+1)(x+2)}=\dfrac{A}{x+1}+\dfrac{B}{x+2}$ gives $A=1,\ B=-1$.
2. So integrand $=\dfrac{1}{x+1}-\dfrac{1}{x+2}$.
3. Integrate: $\log|x+1|-\log|x+2|$.
4. Combine: $\log\left|\dfrac{x+1}{x+2}\right|+C$. Option A inverts the ratio.
_Source: syllabus Mathematics Ch 7 "Integrals", p.317_
Keep practising Probability & Statistics
Browse all Probability & Statistics questions for AP Intermediate 1st Year, or explore more Mathematics topics.
Related questions
$\int x\cos x\,dx$ equalsThe integration-by-parts formula $\int u\,\dfrac{dv}{dx}\,dx$ equals$\int \dfrac{dx}{x(x^2+1)}$ equals$\int \dfrac{x\,dx}{(x-1)(x-2)}$ equalsIn decomposing $\dfrac{1}{(x+1)(x+2)}=\dfrac{A}{x+1}+\dfrac{B}{x+2}$, the constants are$\int \dfrac{dx}{x^2+2x+2}$ equals$\int \dfrac{dx}{x^2-6x+13}$ equals$\int \dfrac{dx}{ qrt{2x-x^2}}$ equals