ज्ञात करें `int x tan^(-1) x dx`

Explanation

यहाँ x, algebraic function है तथा `tan^(-1)x` , inverse trigonoetric function है तथा ILATE me I, A के पहले है अतः `tan^(-1)x` को u मन्ना होगा |
`I = int x tan^(-1) x dx = ( tan^(-1)x) x^2/2 - int (1/(1+x^2) x^2/2)dx`
`x^2/ x tan^(-1) x -1/2 int x^2/(1+x^2)dx = x^2/ 2 tan^(-1) x -1/2 int (1+x^2 -1)/(1+x^2)dx`
`x^2/x tan^(-1) x - 1/2 int ( 1 -""1/(1+x^2)) dx = x^2/ 2 tan^(-1) x - 1/2 (x - tan^(-1) x)+c`
`=x^2/2 tan^(-1) x-x/2+(tan^(-1)x)/2+c`