1 ________
/ / 1
| a* / 1 + -- 2 /1\
| _________ / 2 a *asinh|-|
| / 2 2 \/ a \a/
| \/ a + x dx = --------------- + -----------
| 2 2
/
0
$$\int_{0}^{1} \sqrt{a^{2} + x^{2}}\, dx = \frac{a^{2}}{2} \operatorname{asinh}{\left (\frac{1}{a} \right )} + \frac{a}{2} \sqrt{1 + \frac{1}{a^{2}}}$$
Ответ (Неопределённый)
[src] ________
/ 2
/ / x
| 2 /x\ a*x* / 1 + --
| _________ a *asinh|-| / 2
| / 2 2 \a/ \/ a
| \/ a + x dx = C + ----------- + ------------------
| 2 2
/
$${{a^2\,{\rm asinh}\; \left({{x}\over{\left| a\right| }}\right)
}\over{2}}+{{x\,\sqrt{x^2+a^2}}\over{2}}$$