Đáp án:
• \( F(x) = \int x\sqrt{1+x^2} \, dx = \frac{1}{2} \int (2x(1+x^2)^{\frac{1}{2}}) \, dx \)
\( = \frac{1}{2} \frac{(1+x^2)^{\frac{3}{2}}}{\frac{3}{2}} + C = \frac{1}{3} (1+x^2)\sqrt{1+x^2} + C \)
• \( F(\sqrt{3}) = \frac{8}{3} + C = 2 \implies C = -\frac{2}{3} \)
• Vậy chọn đáp án \(\boxed{\text{A}} \)
Thêm:
• \( \int \cos x \sqrt{1+2\sin x} \, dx \)
• \( \int x^3 (1+x^4)^5 \, dx \)