What is the integral of e^{(x+y)} ?

The integral of e^{(x+y)} is e^{y+x}+C

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integral of e^{(x+y)}

\int e^{(x + y)}

e^{y + x} + C

Solution steps

\int e^{x + y} d x

e^{y + x} = e^{y} e^{x}

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

Take the constant out:

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

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

Use the common integral:

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

= e^{y} e^{x}

Apply exponent rule:

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

e^{y} e^{x} = e^{y + x}

= e^{y + x}

Add a constant to the solution

= e^{y + x} + C

x y^{2} y^{^{'}} = x + 8

\int \frac{2 x}{4 x ^{4} - 9} d x

\int (6 x + 1) (6 x^{2} + 2 x)^{\frac{3}{4}} d x

\frac{d}{d x} (\frac{5}{x + 8})

y = 3 x, y = \frac{3}{x}, x = 4