a) \(\int\frac{dx}{\sqrt[3]{5x}}=\frac{1}{\sqrt[3]{5}}\int x^{-\frac{1}{3}}dx=\frac{1}{\sqrt[3]{5}}.\frac{3}{2}.x^{\frac{2}{3}}+C=\frac{3}{2\sqrt[3]{5}}+C\)
b) Nhân và chia nguyên hàm cho -2 ta có :
\(\int e^{-\frac{x}{2}}=-2\int e^{-\frac{x}{2}}d\left(-\frac{x}{2}\right)=-2e^{-\frac{x}{2}}+C\)
c) \(\int\sin\left(ax+b\right)dx=\frac{1}{a}\int\sin\left(ax+b\right)d\left(ax+b\right)=-\frac{1}{a}\cos\left(ax+b\right)+C\)
d) \(\int\frac{dx}{5x+4}=\frac{1}{5}\int\frac{5}{5x+4}dx=\frac{1}{5}\int\frac{d\left(5x+\text{4}\right)}{5x+4}=\frac{1}{5}\ln\left|5x+4\right|+C\)
Tích phân này có thể tính cách khác :
\(\int\frac{dx}{5x+4}=\frac{1}{5}\int\frac{1}{x+\frac{4}{5}}dx=\frac{1}{5}\int\frac{d\left(x+\frac{4}{5}\right)}{x+\frac{4}{5}}=\frac{1}{5}\ln\left|x+\frac{4}{5}\right|+C\)