Question

सोडवा: `int 1/(x(x^6 + 1))` dx

Answer 1

I = `int 1/(x(x^6 + 1))` dx मानू

`= int x^5/(x^6(x^6 + 1))`dx

x⁶ = t ठेवू

∴ 6x⁵ dx = dt

∴ `x^5 * dx = 1/6 * dt`

∴ I = `1/6 int dt/(t(t + 1))`

`= 1/6 int ((t + 1) - t)/(t(t + 1))` dt

`= 1/6 int (1/t - 1/(t + 1))` dt

= `1/6` [log | t | – log |t + 1|] + c

`= 1/6 log |t/(t + 1)|` + c

∴ I = `1/6 log |x^6/(x^6 + 1)|` + c