indefinite integrals

∫dxx22(x7-6)

plzzz solve this frnds...

7 Answers

1
ARKA(REEK) ·

Take 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 ...

1
जय ·

gr8 arka................

1
ARKA(REEK) ·

Process 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 ...

1
ARKA(REEK) ·

Will any body please have a look at the solutions ... and check if there is any mistake ... ????

1
ARKA(REEK) ·

This 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 ...

1
ARKA(REEK) ·

Nishant sir ... please check my solutions ...

1
abhishek557 singh ·

∫7xdx

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