What is the integral of x^4e^{xz}-2zsin(z^2) ?

The integral of x^4e^{xz}-2zsin(z^2) is x^3e^{xz}+cos(z^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^4e^{xz}-2zsin(z^2)

\int x^{4} e^{x z} - 2 z sin (z^{2}) d z

x^{3} e^{x z} + cos (z^{2}) + C

Solution steps

\int x^{4} e^{x z} - 2 z sin (z^{2}) d z

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{4} e^{x z} d z - \int 2 sin (z^{2}) z d z

\int x^{4} e^{x z} d z = x^{3} e^{x z}

\int 2 sin (z^{2}) z d z = - cos (z^{2})

= x^{3} e^{x z} - (- cos (z^{2}))

Simplify

= x^{3} e^{x z} + cos (z^{2})

Add a constant to the solution

= x^{3} e^{x z} + cos (z^{2}) + C

\int sec^{6} (3 x) tan (3 x) d x

\int x sin^{2} (x^{\frac{3}{2}} - 4) d x

n = 0 \sum \infty (- \frac{3}{4})^{n}

y = 3 x + 1, (0, 3)

\frac{x d y}{d x} = 3 x e^{x} - y + 6 x^{2}

What is the integral of x^4e^{xz}-2zsin(z^2) ?
The integral of x^4e^{xz}-2zsin(z^2) is x^3e^{xz}+cos(z^2)+C