What is the integral of e^{x^3}(3x^2y-x^2) ?

The integral of e^{x^3}(3x^2y-x^2) is -1/3 e^{x^3}+ye^{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 e^{x^3}(3x^2y-x^2)

\int e^{x^{3}} (3 x^{2} y - x^{2}) d x

- \frac{1}{3} e^{x^{3}} + y e^{x^{3}} + C

Solution steps

\int e^{x^{3}} (3 x^{2} y - x^{2}) d x

Expand

(- x^{2} + 3 y x^{2}) e^{x^{3}} : - e^{x^{3}} x^{2} + 3 y e^{x^{3}} x^{2}

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

Apply the Sum Rule:

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

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

\int e^{x^{3}} x^{2} d x = \frac{1}{3} e^{x^{3}}

\int 3 y e^{x^{3}} x^{2} d x = y e^{x^{3}}

= - \frac{1}{3} e^{x^{3}} + y e^{x^{3}}

Add a constant to the solution

= - \frac{1}{3} e^{x^{3}} + y e^{x^{3}} + C

\int 3 t^{2} - 1 d t

\int e^{x} 43 + e^{x} d x

\int 3.4 (1 - e^{- 2.1 x}) d x

\int e^{x} x sin (x) d x

\int \frac{3}{4 - 5 x} d x

What is the integral of e^{x^3}(3x^2y-x^2) ?
The integral of e^{x^3}(3x^2y-x^2) is -1/3 e^{x^3}+ye^{x^3}+C