Tích phân \(\int\limits^1_0\left(1+3x\right)^{\dfrac{3}{2}}\text{d}x\) bằng
\(\dfrac{62}{15}\).\(4\).\(\dfrac{62}{5}\).\(\dfrac{155}{2}\).Hướng dẫn giải:\(\int\limits^1_0\left(1+3x\right)^{\frac{3}{2}}\text{d}x\)\(=\dfrac{1}{3}\int\limits^1_0\left(1+3x\right)^{\frac{3}{2}}\text{d}\left(1+3x\right)\)
\(=\dfrac{2}{15}\left(1+3x\right)^{\frac{5}{2}}|^1_0\) \(=\dfrac{62}{15}\).