What is the integral of (5tan^2(x)sec^2(x)+13) ?

The integral of (5tan^2(x)sec^2(x)+13) is 5/3 tan^3(x)+13x+C

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integral of (5tan^2(x)sec^2(x)+13)

\int (5 tan^{2} (x) sec^{2} (x) + 13) d x

\frac{5}{3} tan^{3} (x) + 13 x + C

Solution steps

\int 5 tan^{2} (x) sec^{2} (x) + 13 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 5 tan^{2} (x) sec^{2} (x) d x + \int 13 d x

\int 5 tan^{2} (x) sec^{2} (x) d x = \frac{5}{3} tan^{3} (x)

\int 13 d x = 13 x

= \frac{5}{3} tan^{3} (x) + 13 x

Add a constant to the solution

= \frac{5}{3} tan^{3} (x) + 13 x + C

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What is the integral of (5tan^2(x)sec^2(x)+13) ?
The integral of (5tan^2(x)sec^2(x)+13) is 5/3 tan^3(x)+13x+C