What is the integral of (6e^x+7/x) ?

The integral of (6e^x+7/x) is 6e^x+7ln|x|+C

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integral of (6e^x+7/x)

\int (6 e^{x} + \frac{7}{x}) d x

6 e^{x} + 7 ln ∣ x ∣ + C

Solution steps

\int 6 e^{x} + \frac{7}{x} 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 6 e^{x} d x + \int \frac{7}{x} d x

\int 6 e^{x} d x = 6 e^{x}

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= 6 e^{x} + 7 ln ∣ x ∣

Add a constant to the solution

= 6 e^{x} + 7 ln ∣ x ∣ + C

\int y^{3} + 1.8 y^{2} - 2.4 y d y

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

\frac{\partial}{\partial y} (\frac{x y}{x + y + z})

\frac{\partial}{\partial y} (2 x y - y)

f (x) = \frac{7}{x}

What is the integral of (6e^x+7/x) ?
The integral of (6e^x+7/x) is 6e^x+7ln|x|+C