# I haven't seen it before-1

Calculus Level 5

$\large\mathfrak{T}=\displaystyle\int_0^{\pi/6}\left(\sum_{r=1}^{\infty}(-1)^{r+1}\cos x\sin^rx\right)\mathrm{d}x$

If $$\large\mathfrak T$$ can be expressed in the form $$\large\ln\left(\dfrac{\alpha e^{\frac{1}{\psi}}}{\gamma}\right)$$, where $$\alpha,\psi,\gamma$$ are primes, then:

$\Large \alpha\times \psi\times \gamma=\ ?$

Details and Assumptions:-

$$\large e$$ is the Euler's number defined as: $\displaystyle e = \lim_{n\to\infty} \left( 1 + \dfrac{1}{n} \right)^n$

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