What is the integral of (4x+7)e^x ?

The integral of (4x+7)e^x is 4e^xx+3e^x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4x+7)e^x

\int (4 x + 7) e^{x} d x

4 e^{x} x + 3 e^{x} + C

Solution steps

\int (4 x + 7) e^{x} d x

Apply Integration By Parts

: (4 x + 7) e^{x} - \int 4 e^{x} d x

= (4 x + 7) e^{x} - \int 4 e^{x} d x

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

= (4 x + 7) e^{x} - 4 e^{x}

Simplify

(4 x + 7) e^{x} - 4 e^{x} : 4 e^{x} x + 3 e^{x}

= 4 e^{x} x + 3 e^{x}

Add a constant to the solution

= 4 e^{x} x + 3 e^{x} + C

\int 30 x^{29} d x

\frac{d ^{2}}{d x ^{2}} (\frac{3 x + 2}{2 x - 5})

25 y^{^{''}} - 20 y^{^{'}} + 4 y = 0, y (5) = 0, y^{^{'}} (0) = - e^{2}

x = y^{2} + 1, x = y + 3

\frac{\partial}{\partial x} (6 x - 6 y + 5 x y)