integral from 0 to cos(x) of 3^{x^2}

解

\int_{0}^{c o s (x)} 3^{x^{2}} d x

\frac{π erfi ( ln ( 3 ) cos ( x ) )}{2 ln ( 3 )}

解答ステップ

\int_{0}^{c o s (x)} 3^{x^{2}} d x

非初等積分を使用する:

\int 3^{x^{2}} d x = \frac{π erfi ( x ln ( 3 ) )}{2 ln ( 3 )}

= \frac{π erfi ( x ln ( 3 ) )}{2 ln ( 3 )}_{0}^{c o s (x)}

限度を計算する:

\frac{π}{2 ln ( 3 )} erfi (ln (3) cos (x))

= \frac{π}{2 ln ( 3 )} erfi (ln (3) cos (x))

簡素化

= \frac{π erfi ( ln ( 3 ) cos ( x ) )}{2 ln ( 3 )}