✓ Board-verified
Mathematics · 2026 · 3 marks
CBSE 2026 · Region 2 · Set 2 · Q30
Find: ∫ (2 x+1)/(√(6 x+x^2)) d x
Find : $\displaystyle \int \frac{2 x+1}{\sqrt{6 x+x^{2}}} \mathrm{~d} x$
Marking-scheme solution
$\displaystyle I=\int \dfrac{2x+1}{\sqrt{6x+x^{2}}}\, dx$
Let $\displaystyle 2x+1=A(6+2x)+B$
$\displaystyle \Rightarrow A=1, B=-5$
$\displaystyle \therefore I=\int \dfrac{6+2x}{\sqrt{6x+x^{2}}}\, dx-5 \int \dfrac{1}{\sqrt{6x+x^{2}}}\, dx$
$\displaystyle =2\sqrt{6x+x^{2}}-5 \int \dfrac{1}{\sqrt{(x+3)^{2}-3^{2}}}\, dx$
$\displaystyle =2\sqrt{6x+x^{2}}-5 \log\left|(x+3)+\sqrt{6x+x^{2}}\right|+C$
More from Integrals
- Evaluate: ∫_0^π x/(1+ sin x) d x2022 · asked 2×
- Evaluate ∫_-1^1|x^4-x| d x. OR Find ∫ (sin^-1 x)/((1-x^2)^3 / 2) d x.2023
- Find: ∫ (x^2)/((x^2+4)(x^2+9)) d x2023
- Evaluate: ∫_0^π (sin^2026 x)/(sin^2026 x+ cos^2026 x) d x2026
- Evaluate: ∫_1^3 (√x)/(√x+√(4-x)) dx2022
- Find: ∫ ((3 cos x-2) sin x)/(5- sin^2 x-4 cos x) d x OR Evaluate: ∫_-2^2 (x^3+|x|+1)/(x^2+4|x|+4) d x2024
- ∫ (x+5)/((x+6)^2) e^x dx is equal to:2025
- Evaluate ∫ 1/((e^x+e^-x)(e^x-e^-x)) d x log √22023
CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.