What is the integral of e^{cos^2(x)}sin(2x) ?

The integral of e^{cos^2(x)}sin(2x) is -e^{cos^2(x)}+C

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integral of e^{cos^2(x)}sin(2x)

\int e^{c o s^{2} (x)} sin (2 x) d x

- e^{c o s^{2} (x)} + C

Solution steps

\int e^{c o s^{2} (x)} sin (2 x) d x

Apply u-substitution

: \int - 1 d u

= \int - 1 d u

Integral of a constant:

\int a d x = a x

= (- 1) u

Substitute back

u = e^{c o s^{2} (x)}

= (- 1) e^{c o s^{2} (x)}

Simplify

= - e^{c o s^{2} (x)}

Add a constant to the solution

= - e^{c o s^{2} (x)} + C

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What is the integral of e^{cos^2(x)}sin(2x) ?
The integral of e^{cos^2(x)}sin(2x) is -e^{cos^2(x)}+C