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

The integral of 2xe^{x^2}csc^2(e^{x^2}) is -cot(e^{x^2})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2xe^{x^2}csc^2(e^{x^2})

\int 2 x e^{x^{2}} csc^{2} (e^{x^{2}}) d x

- cot (e^{x^{2}}) + C

Solution steps

\int 2 x e^{x^{2}} csc^{2} (e^{x^{2}}) d x

Take the constant out:

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

= 2 \cdot \int x e^{x^{2}} csc^{2} (e^{x^{2}}) d x

Apply u-substitution

: \int \frac{csc ^{2} ( u )}{2} d u

= 2 \cdot \int \frac{csc ^{2} ( u )}{2} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int csc^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= 2 \cdot \frac{1}{2} (- cot (u))

Substitute back

u = e^{x^{2}}

= 2 \cdot \frac{1}{2} (- cot (e^{x^{2}}))

Simplify

2 \cdot \frac{1}{2} (- cot (e^{x^{2}})) : - cot (e^{x^{2}})

= - cot (e^{x^{2}})

Add a constant to the solution

= - cot (e^{x^{2}}) + C

x y^{^{'}} = y + x^{2}

x \to - 7 - lim (\frac{1}{x ^{2} - 49})

\int_{0}^{5} 3 f (x) d x

\frac{d y}{d x} = \frac{7 x}{y}

What is the integral of 2xe^{x^2}csc^2(e^{x^2}) ?
The integral of 2xe^{x^2}csc^2(e^{x^2}) is -cot(e^{x^2})+C