I understand how you would differentiate it, but how would you integrate it?
After plugging it into integral calculator, it says that it is non-elemetary, what does this mean too?
How do you integrate $9^{\sin x}$
calculusintegration
calculusintegration
I understand how you would differentiate it, but how would you integrate it?
After plugging it into integral calculator, it says that it is non-elemetary, what does this mean too?
Best Answer
It does not have any closed-form. What we know is $$\int _{x=0}^{2\pi} 9^{\sin(x)} \mathrm{d} x=\int _{x=0}^{2\pi} e^{\ln(9)\sin(x)} \mathrm{d} x=\mathrm{I}_0(\ln(9)),$$ where $\mathrm{I}_0(\cdot)$ is the modified Bessel function of the first kind.