What is the integral of (5^y+(6x)/(y+4)) ?

The integral of (5^y+(6x)/(y+4)) is 5^yx+(3x^2)/(4+y)+C

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integral of (5^y+(6x)/(y+4))

\int (5^{y} + \frac{6 x}{y + 4}) d x

5^{y} x + \frac{3 x ^{2}}{4 + y} + C

Solution steps

\int 5^{y} + \frac{6 x}{y + 4} 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 5^{y} d x + \int \frac{6 x}{4 + y} d x

\int 5^{y} d x = 5^{y} x

\int \frac{6 x}{4 + y} d x = \frac{3 x ^{2}}{4 + y}

= 5^{y} x + \frac{3 x ^{2}}{4 + y}

Add a constant to the solution

= 5^{y} x + \frac{3 x ^{2}}{4 + y} + C

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What is the integral of (5^y+(6x)/(y+4)) ?
The integral of (5^y+(6x)/(y+4)) is 5^yx+(3x^2)/(4+y)+C