Trong các khẳng định sau, khẳng định nào sai ?
\(\int\limits\sin^2\dfrac{x}{2}\text{d}x=\dfrac{x+\sin x}{2}+C\).\(\int\limits\left(3-2x\right)^4\text{d}x=\dfrac{-\left(3-2x\right)^5}{10}+C\).\(\int\limits\sqrt{4x-1}\text{d}x=\dfrac{1}{6}\sqrt{\left(4x-1\right)^3}+C\).\(\int\limits\sqrt[3]{5-6x}\text{d}x=-\dfrac{1}{8}\sqrt[3]{\left(5-6x\right)^4}+C\).Hướng dẫn giải:
Có \(\left(\dfrac{x+\sin x}{2}+C\right)'=\dfrac{1}{2}\left(1+\cos x\right)=\cos^2x\ne\sin^2x\) nên \(\int\limits\sin^2\dfrac{x}{2}\text{d}x=\dfrac{x+\sin x}{2}+C\) sai.
