Math / Calculus

QuestionДля вычисления этого интеграла вы сделали замену. Чему равен dx? $\int \cos (3 x+5) d x$
Ответ записать в строку без пробелов и скобок. Знак умножения не пишем. Знак деления: /

Studdy Solution

STEP 1

1. We are given the integral $\int \cos (3x+5) \, dx$ .
2. We need to perform a substitution to simplify the integral.
3. The substitution will involve setting a new variable $u$ equal to the expression inside the cosine function.

STEP 2

1. Identify the substitution.
2. Differentiate the substitution to find $dx$ in terms of $du$ .

STEP 3

Identify the substitution:
Let $u = 3x + 5$ .

STEP 4

Differentiate the substitution to find $dx$ in terms of $du$ :
Differentiate both sides of the equation $u = 3x + 5$ with respect to $x$ :
$\frac{du}{dx} = 3$
Solve for $dx$ :
$dx = \frac{du}{3}$
The expression for $dx$ is $du/3$ .

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