What is the integral of xcosh(x^2)sinh(x^2) ?

The integral of xcosh(x^2)sinh(x^2) is 1/8 cosh(2x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of xcosh(x^2)sinh(x^2)

\int x cosh (x^{2}) sinh (x^{2}) d x

\frac{1}{8} cosh (2 x^{2}) + C

Solution steps

\int x cosh (x^{2}) sinh (x^{2}) d x

Rewrite using trig identities

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

Take the constant out:

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

= \frac{1}{2} \cdot \int x sinh (2 x^{2}) d x

Apply u-substitution

= \frac{1}{2} \cdot \int \frac{sinh ( u )}{4} d u

Take the constant out:

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

= \frac{1}{2} \cdot \frac{1}{4} \cdot \int sinh (u) d u

Use the common integral:

\int sinh (u) d u = cosh (u)

= \frac{1}{2} \cdot \frac{1}{4} cosh (u)

Substitute back

u = 2 x^{2}

= \frac{1}{2} \cdot \frac{1}{4} cosh (2 x^{2})

Simplify

\frac{1}{2} \cdot \frac{1}{4} cosh (2 x^{2}) : \frac{1}{8} cosh (2 x^{2})

= \frac{1}{8} cosh (2 x^{2})

Add a constant to the solution

= \frac{1}{8} cosh (2 x^{2}) + C

\int - \frac{2}{sin ( x )} d x

\int coth^{2} (3 x) d x

\int \frac{e ^{2 x}}{1 + 5 e ^{2 x}} d x

\int \frac{1}{x ^{4} x ^{2} - 9} d x

\int \frac{( cos ( θ ) + tan ( θ ) )}{cos ^{2} ( θ )} d θ

What is the integral of xcosh(x^2)sinh(x^2) ?
The integral of xcosh(x^2)sinh(x^2) is 1/8 cosh(2x^2)+C