MCQ
The value of $\int(x+3)(x+2) d x$ is:
- ✓$\frac{x^3}{3}+\frac{5 x^2}{2}+2 x+C$
- B$x^3+\frac{5}{2} x^2+x+C$
- C$\frac{x^3}{3}+\frac{x^2}{2}+2 x+C$
- D$\frac{x^3}{3}+\frac{x^2}{2}+x+C$
✓
Answer
Correct option: A.
$\frac{x^3}{3}+\frac{5 x^2}{2}+2 x+C$
(A) $x^3+\frac{5}{2} x^2+x+C$
Explanation: Let
$\begin{aligned} I & =\int(x+3)(x+2) d x \\ & =\int\left(x^2+5 x+2\right) d x \\ & =\int x^2 d x+5 \int x d x+2 \int d x \\ & =\frac{x^3}{3}+\frac{5 x^2}{2}+2 x+C\end{aligned}$
Explanation: Let
$\begin{aligned} I & =\int(x+3)(x+2) d x \\ & =\int\left(x^2+5 x+2\right) d x \\ & =\int x^2 d x+5 \int x d x+2 \int d x \\ & =\frac{x^3}{3}+\frac{5 x^2}{2}+2 x+C\end{aligned}$
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