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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

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

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

Apply u-substitution

: \int e^{v} \cdot 2 d v

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} \cdot 2 e^{v}

Substitute back

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

Simplify

\frac{1}{2} \cdot 2 e^{\frac{1 - c o s ( 2 x )}{2}} : e^{s i n^{2} (x)}

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

Add a constant to the solution

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

\int_{\frac{1}{2}}^{1} \frac{3}{x 2 - x} d x

\int \frac{1}{( x - 1 ) x ^{2} - 2 x} d x

5 x

y = 8 e x cos (x)

\int_{- \infty}^{0} x e^{6 x} d x

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