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Chapter 5: Q 43. (page 429)

Solve the integral: $\int \frac{3 x + 1}{x} d x$

Short Answer

Expert verified

The required answer is $3 x + \ln (x) + c$ .

Step by step solution

Step 1. Given information

We have given integral is $\int \frac{3 x + 1}{x} d x$ .

Step 2. Solve the integration by parts .

We have,

$\int \frac{3 x + 1}{x} d x = \int (3 + \frac{1}{x}) d x = \int 3 d x + \int \frac{1}{x} d x = 3 x + \ln (x) + c$

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Most popular questions from this chapter

Which of the integrals that follow would be good candidates for trigonometric substitution? If a trigonometric substitution is a good strategy, name the substitution. If another method is a better strategy, explain that method.

$(a) \int \frac{4 + x^{2}}{x} d x$ $(b) \int \frac{x}{4 + x^{2}} d x$

role="math" localid="1648759296940" $(c) \int \frac{x^{2}}{4 + x^{2}} d x$ $(d) \int \frac{16 - x^{4}}{4 + x^{2}} d x$

Solve each of the integrals in Exercises 39–74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

$\int x \sqrt{x^{2} + 1} d x$

For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.

$\int \frac{1}{\sqrt{u}} d u$

Find three integrals in Exercises 39–74 that can be solved without using trigonometric substitution.

Solve given definite integral.

$\int_{0}^{4} x^{3} \sqrt{x^{2} + 4} d x$

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Solve the integral:∫3x+1xdx

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the integration by parts .

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Most popular questions from this chapter

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Solve the integral: $\int \frac{3 x + 1}{x} d x$