Question

assignment 10: problem 11 (1 point) find a particular function which is an indefinite integral for: \\(\int (3x + \sec(x)\tan(x)) dx\\)

Explanation:

Step1: Integrate \(3x\)

The integral of \(ax^n\) is \(\frac{a}{n + 1}x^{n+1}\). For \(3x\) (where \(a = 3\), \(n = 1\)), we have \(\int 3x\ dx=\frac{3}{2}x^2\).

Step2: Integrate \(\sec(x)\tan(x)\)

Recall that the derivative of \(\sec(x)\) is \(\sec(x)\tan(x)\), so \(\int \sec(x)\tan(x)\ dx=\sec(x)\).

Step3: Combine results

Add the two integrals together (and we can ignore the constant of integration for a particular solution). So the particular function is \(\frac{3}{2}x^2+\sec(x)\).

Answer:

\(\frac{3}{2}x^2 + \sec(x)\)