1Take x7 = z
7x6 dx = dz ...
Therefore the expr. can be written as ...
17∫7x6 dxx22*x6(x7 - 6)
Now x22*x6 = x28 = z4
Therefore ... the expr. boils down to ...
17*6∫dzz4(z - 6)
Now .. the expr. can be further simplified as ..
17∫z - (z - 6) dzz4(z - 6)
17*6∫dzz3(z - 6) - 17*6∫dzz - 6 ....
Now proceed likewise ... to get the ans ...
1Process 2 :
The expr. can also be written as ...
∫dxx29(1 - x-7)
Now x-7 can be taken as z
-7x-8 dx = dz
=-17∫-7x-8 dxx29*x-8(1 - x-7)
Now x-21 = z3
So the expr. can be rewritten as ....
= -17∫z3 dz(1 - z)
= 17∫[(1 - z3) - 1] dz(1 - z)
Now ... (1 - z3) can be simplified into (1 - z)[(1 - z)2 + 3z] ... hence the expr. becomes ....
= 17∫(1 + z + z2) dz - 17∫dz1 - z
Now this expr. can be easily evaluated to get the ans ....
I hope ... this is easier to calculate than the previous process ...
1Will any body please have a look at the solutions ... and check if there is any mistake ... ????
1This sum can be done in yet another process ....
Process 3 :
∫dxx21+1(x7 - 6)
∫dxx21*x(x7 - 6)
Now x7 can be taken as z7
Therefore ..... x6 dx = z6 dz
The expr. can be rewritten as ...
∫x6 dxx21*x*x6(x7 - 6)
The expr. hence boils down to ....
∫z6 dzz3*z(z - 6)
The expr. can be further simplified ....
∫z2 dz(z - 6)
∫(z2 - 36 + 36) dz(z - 6)
The ultimate expr. is ...
∫(z + 6) dz + 36∫dzz - 6
I hope ... this process is easier than the previous 2 processes ....
Hope there r no calculation errors ... if there r any ... please pardon me ...