<s>[INST] Compute antiderivative of $x \frac{3}{4} \sqrt{ -x}$ I need to compute the area under $x \times\frac{3}{4} \times \sqrt{|x|}$ from x=-1 to x=1. Therefore I need to compute the antiderivative of $x \times \frac{3}{4} \times \sqrt{x} $ for $0 \le x \le 1$, which is straight forward, $ \frac{3}{10} \times x^{2.5}$. And for $ -1 \le x \le 0 $ I need to compute the antiderivative of $x \frac{3}{4} \sqrt{ -x}$. I am stuck on how to rewrite $x $ and $ \sqrt{ -x}$ as a single term. 
 [/INST] $x\frac34\sqrt{|x|}$ is an odd function - so the integral from -1 to 1 is zero. 
</s>