tìm nguyên hàm: a. ∫2x(1+3x^3)dx b. f(x)=(x-1)/(2x-1)

$\begin{array}{l}a)\quad \displaystyle\int2x(1 + 3x^3)dx\\ = 2\displaystyle\int xdx + 6\displaystyle\int x^4dx\\ = 2\cdot\dfrac{x^2}{2} + 6\cdot\dfrac{x^5}{5} + C\\ = x^2 + \dfrac{6x^5}{5} + C\\ b)\quad \displaystyle\int\dfrac{x-1}{2x-1}dx\\ = \displaystyle\int\left[\dfrac12 – \dfrac{1}{2(2x-1)}\right]dx\\ = \dfrac12\displaystyle\int dx – \dfrac12\displaystyle\int\dfrac{1}{2x-1}dx\\ = \dfrac12x – \dfrac14\displaystyle\int\dfrac{d(2x-1)}{2x-1}\\ = \dfrac12x-\dfrac14\ln|2x-1| + C \end{array}$