What is the integral of 5x^2cosh(x^3) ?

The integral of 5x^2cosh(x^3) is 5/3 sinh(x^3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5x^2cosh(x^3)

\int 5 x^{2} cosh (x^{3}) d x

\frac{5}{3} sinh (x^{3}) + C

Solution steps

\int 5 x^{2} cosh (x^{3}) d x

Take the constant out:

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

= 5 \cdot \int x^{2} cosh (x^{3}) d x

Apply u-substitution

: \int \frac{u cosh ( u ^{\frac{3}{2}} )}{2 x} d u

= 5 \cdot \int \frac{cosh ( u )}{3} d u

Take the constant out:

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

= 5 \cdot \frac{1}{3} \cdot \int cosh (u) d u

Use the common integral:

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

= 5 \cdot \frac{1}{3} sinh (u)

Substitute back

u = x^{3}

= 5 \cdot \frac{1}{3} sinh (x^{3})

Simplify

5 \cdot \frac{1}{3} sinh (x^{3}) : \frac{5}{3} sinh (x^{3})

= \frac{5}{3} sinh (x^{3})

Add a constant to the solution

= \frac{5}{3} sinh (x^{3}) + C

\int (4 e^{z} + 15 - \frac{1}{6 z}) d z

\int (x + 2) e^{x^{2} + 4 x} d x

\int \frac{π}{x ln ( x )} d x

\int \frac{3 x}{2} - \frac{9}{4 x} + 2 d x

\int 5 (x^{4} + 5)^{5} d x

What is the integral of 5x^2cosh(x^3) ?
The integral of 5x^2cosh(x^3) is 5/3 sinh(x^3)+C