Resuelve las siguientes integrales:

2018

1. \(\int_{\pi}^{2\pi} (2cosx+|x-1|)\,dx\)
2. \(\int_{2}^{4} ((6-x)e^{\dfrac{x-4}{3}}\,dx\)

2017

1. \(\int_{1}^2\ f(x)\,dx \text{ siendo } f(x)=\left\{\begin{array}{rcl}\dfrac{sin(2x)}{x} & \text{si} & x < 0\\ xe^x+2 & \text{si} & x \ge 0\\ \end{array}\right.\)
2. \(\int_{-1}^0\ f(x)\,dx \text{ siendo } f(x)=\left\{\begin{array}{rcl}xe^{2x} & \text{si} & x < 0\\ \frac{ln(x+1)}{x+1} & \text{si} & x \ge 0\\ \end{array}\right.\)
3. \(\int (3u+1)cos(2u)\,du\)
4. \(\int_{2}^{5} \dfrac{7}{4x+1}\,dx\)
5. \(\int \dfrac{1}{x+2}-\dfrac{1}{x-4}\,dx\)
6. \(\int_{1}^{2} (\dfrac{2}{x}+x-3)\,dx\)
7. \(\int_{3}^{5} \dfrac{x^2+x+6}{x-2}\,dx\)
8. \(\int_{1}^{3} xe^{-x}\,dx\)
9. \(\int_{0}^{1} ((x-1)e^x-x+1)\,dx\)

2016

1. \(\int_{0}^{\sqrt{3}} (2+x-x^2-\dfrac{2}{x+1})\,dx\)
2. \(\int_0^6 \left( 2x^2-\dfrac{x^3}{3}\right)^2\,dx\)
3. \(\int_{-1}^1\ f(x)\,dx \text{ siendo } f(x)=\left\{\begin{array}{rcl} \frac{1}{5-x} & \text{si} & x \le 0\\\frac{1}{5+x} & \text{si} & x > 0\\ \end{array}\right.\)
4. \(\int_{-1}^1 \frac{9}{2x-4}+2x-1\,dx\)
5. \(\int_{-1}^1\ f(x)\,dx \text{ siendo } f(x)=\left\{\begin{array}{rcl} \frac{ln(1-x)}{1-x} & \text{si} & x < 0\\ xe^{-x}& \text{si} & x \ge 0\\ \end{array}\right.\)
6. \(\int_{-1}^1\ f(x)\,dx \text{ siendo } f(x)=\left\{\begin{array}{rcl} |x| & \text{si} & x < 1\\ xe^{1-x}& \text{si} & x \ge 1\\ \end{array}\right.\)
7. \(\int_{1}^2\ f(x)\,dx \text{ siendo } f(x)=\left\{\begin{array}{rcl} |x| & \text{si} & x < 1\\ xe^{1-x}& \text{si} & x \ge 1\\ \end{array}\right.\)

2015

1. \(\int_{0}^1 (x-2)\sqrt{x^2-4x+3}\,dx\)
2. \(\int_{-1}^0 x^2e^x\,dx\)
3. \(\int_1^4 (1-x)e^{-x }\,dx\)
4. \(\int \dfrac{x}{x^2-4}+\dfrac{ln(x+1)}{x+1}\,dx\)
5. \(\int (3x+5)cos{x}\,dx\)
6. \(\int_{-1/2}^{1/2} \dfrac{x^2-4x+3}{x^2-1}\,dx\)
7. \(\int_1^{ln{5}} xe^x+3 \,dx\)