Let

f(x) = ∫ (16x+24)/(x²+2x−15) dx

If:

f(4)=140 log_e(3)

Find f(7).

Factorizing denominator:

x²+2x−15 = (x+5)(x−3)

Applying partial fractions:

(16x+24)/(x²+2x−15) = 4/(x−3) + 12/(x+5)

Integrating:

f(x) = 4ln|x−3| + 12ln|x+5| + C

Using:

f(4)=140ln(3)

and substituting x=7,

the constant cancels and the final value becomes:

f(7) = ln(2³² · 3³⁷)

Final Answer

ln(2³² × 3³⁷)