Integrate the following in the given intervals :

1. f(x)=3x²+6x                    x  ϵ ℝ
2. f(x)=sinx –\(\frac{1}{x^3}\)+\(\frac{1}{x^2}\)    x  ϵ (0, +∞)
3. f(x)=cosx +\(\frac{1}{x^2}\)+\(\frac{1}{x}\)    x  ϵ (0, +∞)

Calculate the following integrals : –

I  = \(\int_{\pi/6}^{\pi/3} sinx~dx\)

J  = \(\int_{\pi/6}^{\pi/3} 7cos x~dx\)

k = \(\int_{0}^{1}xe^{x^2+1}dx\)

L = \(\int_{0}^{\pi/2}3~cos~x~sin^2x dx\)

M = \(\int_{1}^{2}\frac{4x^2 - 1}{8x}dx\)

N = \(\int_{1}^{2} x~Inx~dx\)