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

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

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

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

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

Solution steps

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

x \to 3 lim (\frac{6}{x - 3})

2 x - 3

x \to - 1 - lim (\frac{1}{x + 1})

\frac{d y}{d x} + y = x y^{8}

f (x) = 5 x + 2

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