What is the integral of 5e^{x+5} ?

The integral of 5e^{x+5} is 5e^{5+x}+C

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integral of 5e^{x+5}

\int 5 e^{x + 5} d x

5 e^{5 + x} + C

Solution steps

\int 5 e^{x + 5} d x

Take the constant out:

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

= 5 \cdot \int e^{x + 5} d x

e^{x + 5} = e^{5} e^{x}

= 5 \cdot \int e^{5} e^{x} d x

Take the constant out:

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

= 5 e^{5} \cdot \int e^{x} d x

Use the common integral:

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

= 5 e^{5} e^{x}

Apply exponent rule:

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

e^{5} e^{x} = e^{5 + x}

= 5 e^{5 + x}

Add a constant to the solution

= 5 e^{5 + x} + C

2 t \cdot \frac{d y}{d t} + y = t

\int_{1}^{3} \frac{2}{x ^{2} + 2 x + 1} d x

f (x) = x^{2} + 5, at x = - 2

\frac{16}{4 + x ^{2}}, y = 1

y = \frac{1}{4 - 9 x ^{2}}, (0, \frac{1}{3})