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

The integral of e^{2sin^2(x)}sin(2x) is 1/2 e^{2sin^2(x)}+C

Popular >

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

\int e^{2 s i n^{2} (x)} sin (2 x) d x

\frac{1}{2} e^{2 s i n^{2} (x)} + C

Solution steps

\int e^{2 s i n^{2} (x)} sin (2 x) d x

Rewrite using trig identities

= \int e^{1 - c o s (2 x)} sin (2 x) d x

Apply u-substitution

: \int \frac{e ^{u}}{2} d u

= \int \frac{e ^{u}}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{2} e^{u}

Substitute back

u = 1 - cos (2 x)

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

Rewrite using trig identities

= \frac{1}{2} e^{2 s i n^{2} (x)}

Add a constant to the solution

= \frac{1}{2} e^{2 s i n^{2} (x)} + C

\frac{50}{x}

\int \frac{20}{1 - cos ( 4 x )} d x

x \to 4 lim (\frac{x + 5}{x - 4})

x \to \frac{9}{2} lim (2 x - 7)

\frac{\partial}{\partial y} (y^{2} sin (2 x))

What is the integral of e^{2sin^2(x)}sin(2x) ?
The integral of e^{2sin^2(x)}sin(2x) is 1/2 e^{2sin^2(x)}+C