Question

integrate 1/x^5*(1-x^7)​

Answer 1

ne way to look at the problem is to say that it would be easy if the integrand were

7x6−1x7−x,

and also easy if it were

x6−1x7−x.

Now take a linear combination of these to knock out the x6 term in the numerator.

Answer 2

Answer:

I=∫dxx(x7+1)I=∫dxx(x7+1)

=∫dxx8+x=∫dxx8+x

=∫dxx8(1+1x7)=∫dxx8(1+1x7)

u=1+1x7⟹du=−7dxx8⟹−du7=dxx8u=1+1x7⟹du=−7dxx8⟹−du7=dxx8

I=−17∫1uduI=−17∫1udu

=−ln(u)7=−ln⁡(u)7

=−ln(1+1x7)7+c