不定积分题目：如图以下是我的解法请指教

I have a nice method that don't require you to set up equations
just do some simple substitutions


再问： Excuse me, could you explain more about the integral of
再问： Why d x/(x^2+9)=0?
再答： since the interval of the integral is symmetric about the y - axis together with the integrand x/(x² + 9), which is an odd function that means f(- x) = - f(x), it's rotational symmetric about the origin for the interval [- a，0], the value of the bounded area is negative(or positive) for the interval [0, a], the value of the bounded area is positive(or negative) as a result, the areas cancels each other and the total value of the integral is zero. ∫(- a→a) ƒ(x) dx = 0 if ƒ(x) is an odd function on the contrary, if the integrand is an even function, i.e. f(- x) = f(x) this function is symmetric about the y - axis which means the two areas bounded in the two intevals are totally identical therefore we have ∫(- a→a) ƒ(x) dx = 2∫(0→a) ƒ(x) dx i.e. 1/(x² + 9) is an even function