What is the integral from 0 to cos(x) of 3^{x^2} ?

The integral from 0 to cos(x) of 3^{x^2} is (sqrt(pi)\erfi(sqrt(ln(3))cos(x)))/(2sqrt(ln(3)))

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

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

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

Solution steps

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

Use the nonelementary integral:

\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)}

Compute the boundaries:

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

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

Simplify

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

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\int_{0}^{2} 0.5 x^{2} d x

\int_{0}^{1} x \frac{2 ( x + 1 )}{3} d x

\int_{1}^{1.5} \frac{3}{8} x^{2} d x

What is the integral from 0 to cos(x) of 3^{x^2} ?
The integral from 0 to cos(x) of 3^{x^2} is (sqrt(pi)\erfi(sqrt(ln(3))cos(x)))/(2sqrt(ln(3)))