Evaluate: (i) `intx^3cosx^4\ dx` (ii) `intx^3sinx^4\ dx`

Explanation

`"(i) Let I " intx^(3) " cos" x^(4) " dx "`
`" Let " x^(4) =t`
`rArr " "4x^(2) dx =dt`
`rArr " "x^(3) dx = (dt)/(4)`
`:. " "I = int " cos " x^(4) " dx "`
` = int " cos " .(dt)/(4) =1/4 " sin "t+ c`
` =1/4 " sin " x^(4) +c.`


`"(ii) Let I " intx^(3) " sin" x^(4) " dx "`
`" Let " x^(4) =t`
`rArr " "4x^(2) dx =dt`
`rArr " "x^(3) dx = (dt)/(4)`
`:. " "I = int " sin " x^(4) " dx "`
` = int " sin " .(dt)/(4) =-1/4 " cost "t+ c`
` =-1/4 " cos " x^(4) +c.`