若∫[f'(Inx)\x]dx=sinx+C,则f（x）=?

若∫[f'(Inx)\x]dx=sinx+C,则f（x）=?
若∫[f'(Inx)\x]dx=sinx+C,则f（x）=?

若∫[f'(Inx)\x]dx=sinx+C,则f（x）=?
原式=∫f'(lnx)d(lnx) = sinx + c
∫d[f(lnx)] = sinx +c
f(lnx) = sinx + c,用t = ln(x)代入
所以 f(t) = sin(e^t) + c
即 f(x) = sin(e^x) + c