Consider the function f(x)=∫x3sinxln(t2+1)dtf(x) = \int_{x^3}^{\sin x} \ln(t^2 + 1) dtf(x)=∫x3sinxln(t2+1)dt. What is the expression for f′(x)f'(x)f′(x)?
sinxcosxx2+1−x3x6+1\frac{\sin x \cos x}{x^2+1} - \frac{x^3}{x^6+1}x2+1sinxcosx−x6+1x3
ln((sinx)2+1)−ln(x6+1)\ln((\sin x)^2 + 1) - \ln(x^6 + 1)ln((sinx)2+1)−ln(x6+1)
ln(x2+1)⋅(cosx−3x2)\ln(x^2+1) \cdot (\cos x - 3x^2)ln(x2+1)⋅(cosx−3x2)
ln((sinx)2+1)cosx−ln(x6+1)3x2\ln((\sin x)^2 + 1) \cos x - \ln(x^6 + 1) 3x^2ln((sinx)2+1)cosx−ln(x6+1)3x2