Explanation:
\(\frac{dy}{dx} = \frac{sin(a+y) cosy - siny cos(a+y)}{sin^2(a+y)}\)
\(x = \frac{siny}{sin(a+y)}\)
On differentiating w.r.t. y, we get
\(=\frac{sin(a+y-y)}{sin^2(a+y)}\)
\(\Rightarrow \frac{dy}{dx}=\frac{sin^2(a+y)}{sina}\)
If \[ \int e^x (x^3 + x^2 - x + 4) \, dx = e^x f(x) + C, \] then \( f(1) \) is:
The value of : \( \int \frac{x + 1}{x(1 + xe^x)} dx \).