Integration

1/4 x^4  + 1/48 pi  x^3   + K   <------  Yep, I seem to forget that constant regularly !   

1/4 x^4  + 1/48 pi  x^3

Take the integral:

integral (x^3+x^2/(16 pi)) dx

Integrate the sum term by term and factor out constants:

= integral x^3 dx+1/(16 pi) integral x^2 dx

The integral of x^3 is x^4/4:

= x^4/4+1/(16 pi) integral x^2 dx

The integral of x^2 is x^3/3:

Answer: | = x^4/4+x^3/(48 pi)+constant

Here.....I'm assuming that the last term is being divided by 16pi.......

∫  x^3 +  x^2/16pi  dx  =

∫ x^3 dx  + ∫ x^2/16pi  dx  =

∫ x^3 dx   + [1/16pi ] ∫ x^2 dx  =

x^4 / 4    + [1/16pi] [ x^3]/ 3   + C   =

x^4/4   + x^3 / [ 48pi] + C

My Calc I  teacher would not have been happy with you for leaving out that constant, ElectricPavlov......LOL!!!!!

[She used to mark the whole thing wrong if you did that......believe me......I never made that mistake twice ]

My calc teacher(s) would be unhappy too....likely they are turning over in their graves !        Thanx Chris...     LOL