Question

सोडवा: `int (1)/(25 - 9x^2)*dx`

Answer 1

I = `int (1)/(25 - 9x^2)*dx`

= `int(1)/(5^2 - (3x)^2)*dx`

= `(1)/(2(5))log |(5 + 3x)/(5 - 3x)|*(1)/(3) + c`

= `(1)/(30)log |(5 + 3x)/(5 - 3x)| + c`

पर्यायी पद्धत:

`int (1)/(25 - 9x^2)*dx`

= `(1)/(9) int (1)/((25)/(9)x^2)*dx`

= `(1)/(9) int (1)/((5/3)^2 - x^2)*dx`

= `(1)/(9) xx (1)/(2 xx 5/3)log|(5/3 + x)/(5 / 3 - x)|+ c`

= `(1)/(30)log|(5 + 3x)/(5 - 3x)| + c`