What is the integral of e^{t+2} ?

The integral of e^{t+2} is e^{2+t}+C

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integral of e^{t+2}

\int e^{t + 2} d t

e^{2 + t} + C

Solution steps

\int e^{t + 2} d t

e^{t + 2} = e^{2} e^{t}

= \int e^{2} e^{t} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{2} \cdot \int e^{t} d t

Use the common integral:

\int e^{t} d t = e^{t}

= e^{2} e^{t}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{2} e^{t} = e^{2 + t}

= e^{2 + t}

Add a constant to the solution

= e^{2 + t} + C

\frac{d}{d y} (4 9 - y)

y^{^{'}} = 3 x (x - 1)

x \to 0 - lim (\frac{1}{x} - cot (x))

- x^{2} + 4 x