Step by step solution to "Evaluate the given indefinite integral. ∫3−5xexxdx"

sklicatias

Answered question

2021-11-21

Evaluate the given indefinite integral.

\int \frac{3 - 5 x e^{x}}{x} d x

David Tyson

Beginner2021-11-22Added 19 answers

Step 1
The given integral is

\int \frac{3 - 5 x e^{x}}{x} d x

Step 2
Obtain the value of the given integral as shown below:

\int \frac{3 - 5 x e^{x}}{x} d x = \int \frac{3}{x} d x - \int \frac{5 x e^{x}}{x} d x

= 3 \int \frac{1}{x} d x - 5 \int e^{x} d x

= 3 \ln | x | - 5 e^{x} + C

Alfonso Miller

Beginner2021-11-23Added 20 answers

Step 1: Split fraction.

\int \frac{3}{x} + \frac{- 5 x e^{x}}{x} d x

Step 2: Use Sum Rule:

\int f (x) + g (x) d x = \int f (x) d x + \int g (x) d x

\int \frac{3}{x} d x + \int - 5 e^{x} d x

Step 3: Use Constant Factor Rule:

\int c f (x) d x = c \int f (x) d x

3 \int \frac{1}{x} d x + \int - 5 e^{x} d x

Step 4: The derivative of

\ln x i s \frac{1}{x}

3 \ln x + \int - 5 e^{x} d x

Step 5: Use Constant Factor Rule:

\int c f (x) d x = c \int f (x) d x

3 \ln x - 5 \int e^{x} d x

Step 6: The integral of

e^{x} i s e^{x}

3 \ln x - 5 e^{x}

Step 7: Add constant.

3 \ln x - 5 e^{x} + C

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