What is the integral of e^{2x}(x^2+3x-1) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{2x}(x^2+3x-1)

\int e^{2 x} (x^{2} + 3 x - 1) d x

\frac{1}{2} e^{2 x} x^{2} + e^{2 x} x - e^{2 x} + C

Solution steps

\int e^{2 x} (x^{2} + 3 x - 1) d x

Apply Integration By Parts

: \frac{1}{2} e^{2 x} (x^{2} + 3 x - 1) - \int e^{2 x} x + \frac{3}{2} e^{2 x} d x

= \frac{1}{2} e^{2 x} (x^{2} + 3 x - 1) - \int e^{2 x} x + \frac{3}{2} e^{2 x} d x

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

= \frac{1}{2} e^{2 x} (x^{2} + 3 x - 1) - (\frac{1}{2} e^{2 x} x + \frac{1}{2} e^{2 x})

Simplify

\frac{1}{2} e^{2 x} (x^{2} + 3 x - 1) - (\frac{1}{2} e^{2 x} x + \frac{1}{2} e^{2 x}) : \frac{1}{2} e^{2 x} x^{2} + e^{2 x} x - e^{2 x}

= \frac{1}{2} e^{2 x} x^{2} + e^{2 x} x - e^{2 x}

Add a constant to the solution

= \frac{1}{2} e^{2 x} x^{2} + e^{2 x} x - e^{2 x} + C

\int (3 - 2 x) cos (5 - 4 x) d x

\int 2^{5 t^{2}} t d t

\int x (ln (x) + 1) d x

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

\int \frac{x}{x ^{2} + 2} 7^{l n (x^{2} + 2)} d x

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