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

The integral of (e^x+2)^2e^x is ((e^x+2)^3)/3+C

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

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

\frac{( e ^{x} + 2 ) ^{3}}{3} + C

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = e^{x} + 2

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

Add a constant to the solution

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

2 sin (3 θ), 1

\frac{d}{d x} (4 e^{2 x} x + 4 e^{2 x})

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

y = x^{3} - 3 x + 1, (2, 3)

\int (in t)^{2} d t

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