Please integrate and show all workings before i will rate it

Please integrate and show all workings before i will rate it.

Integrated the following functions and show all work. (2 + 3x) dx 5x2 / x3 + 2 dx sin 3x dx

Solution

1. Int ( 2+3x) dx = 2 Int dx + 3 Int x dx = 2 x + 3 x^2 +c 2. Put x^3 + 2 =t We\'ll differentiate both sides: x^2=dt Apply this in Question; We get = 5 Int ( 1/Sqrt ( t) ) dt = 5 [ (t) ^ -3/2 ] / (-3/2) + C = - 10/3 [ ( x^3 + 2 )^3/2 ] + C 3. Int sin 3x dx We\'ll substitute 3x by t. 3x = t We\'ll differentiate both sides: 3dx = dt We\'ll divide by 3: dx = dt/3 We\'ll re-write the integral of the function , changing the variable x to t: Int sin t*(dt/3) = (1/3)*Int sin t dt (1/3)*Int sin t dt = - cos t/3 +C We\'ll substitute t by 3x: Int sin 3x dx = - (cos 3x)/3 +C