`int_(0)^((pi)/(4))(2sec^(2)x+x^(3)+2)dx`

Explanation

`int_(0)^(pi//4)(2sec^(2)x+x^(3)+2)dx`
`=2int_(0)^(pi//4)sec^(2)xdx+int_(0)^(pi//4)x^(3)dx+2int_(0)^(pi//4)1dx`
`=2[tanx]_(0)^(pi//4)+(1)/(4)[x]_(0)^(pi//4)+2[x]_(0)^(pi//4)`
`=2tan.(pi)/(4)+(1)/(4)((pi)/(4))^(4)+2((pi)/(4))`
`=2+(pi)/(2)+(pi^(4))/(1024)`