Cho hàm số f(x) liên tục trên R A 0 B -15 C -2 D -13

Đặt: $t=\sqrt{x^2+5}-x\Rightarrow x=\frac{5-t^2}{2t}\Rightarrow \text{d}x=-\left(\frac{1}{2}+\frac{5}{2t^2}\right)\text{d}t$

Ta có: $1=\underset{1}{\overset{5}{\int }}f\left(t\right)\left(\frac{1}{2}+\frac{5}{2t^2}\right)\text{d}t=\frac{1}{2}\underset{1}{\overset{5}{\int }}f\left(t\right)\text{d}t+\frac{5}{2}\underset{1}{\overset{5}{\int }}\frac{f\left(t\right)}{t^2}\text{d}t$

$\Rightarrow \frac{1}{2}\underset{1}{\overset{5}{\int }}f\left(t\right)\text{d}t=1-\frac{5}{2}\underset{1}{\overset{5}{\int }}\frac{f\left(t\right)}{t^2}\text{d}t=1-\frac{5}{2}.3=-\frac{13}{2}$

$\Rightarrow \underset{1}{\overset{5}{\int }}f\left(t\right)\text{d}t=-13$

Chọn đáp án D