If In=∫cos⁡nxsin⁡xdx, then I10−I8 is equal to

I10=∫cos10xsinxdxcos⁡10x−cos⁡8x=−2sin⁡9xsin⁡x⇒cos⁡10x−cos⁡8xsin⁡x=−2sin⁡9x∴∫cos⁡10xsin⁡x−cos⁡8xsin⁡xdx=∫−2sin⁡9xdx⇒I10−I8=−2(−cos⁡9x)9⇒I10−I8=29cos⁡9x+C