6+sin(x)=?6 + \sin(x) = ?

Calculus Level 5

If

0sinx7 dx=sin(πa)Γ(b7)\displaystyle\int_{0}^{\infty} \sin x^7\ dx = \sin \left(\frac{\pi}{a}\right)\Gamma\left({\frac{b}{7}}\right)

Find a+b\boxed{a+b}

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