What is the integral of (3x+2e^x)^2 ?

The integral of (3x+2e^x)^2 is 3x^3+12(e^xx-e^x)+2e^{2x}+C

Popular >

integral of (3x+2e^x)^2

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

3 x^{3} + 12 (e^{x} x - e^{x}) + 2 e^{2 x} + C

Solution steps

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

Expand

(3 x + 2 e^{x})^{2} : 9 x^{2} + 12 e^{x} x + 4 e^{2 x}

= \int 9 x^{2} + 12 e^{x} x + 4 e^{2 x} 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 9 x^{2} d x + \int 12 e^{x} x d x + \int 4 e^{2 x} d x

\int 9 x^{2} d x = 3 x^{3}

\int 12 e^{x} x d x = 12 (e^{x} x - e^{x})

\int 4 e^{2 x} d x = 2 e^{2 x}

= 3 x^{3} + 12 (e^{x} x - e^{x}) + 2 e^{2 x}

Add a constant to the solution

= 3 x^{3} + 12 (e^{x} x - e^{x}) + 2 e^{2 x} + C

\frac{\partial}{\partial x} (5 9 x^{2} + 16 y^{2})

\int \frac{7}{x ( x ^{2} + 25 )} d x

\frac{d ^{2}}{d x ^{2}} (sin (x^{2}))

\int csc^{4} (x) cot^{2} (x) d x

x \to 2 lim (5 x^{3} + x)

What is the integral of (3x+2e^x)^2 ?
The integral of (3x+2e^x)^2 is 3x^3+12(e^xx-e^x)+2e^{2x}+C