What is the integral of sec^2(x)+4 ?

The integral of sec^2(x)+4 is tan(x)+4x+C

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integral of sec^2(x)+4

\int sec^{2} (x) + 4 d x

tan (x) + 4 x + C

Solution steps

\int sec^{2} (x) + 4 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 sec^{2} (x) d x + \int 4 d x

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

\int 4 d x = 4 x

= tan (x) + 4 x

Add a constant to the solution

= tan (x) + 4 x + C

\int e^{x} e^{x} d x

\int \frac{3 x}{x ^{2} - x - 6} d x

\int_{0}^{1} 3 x (x^{2} + 1)^{4} d x

x^{2} \frac{d y}{d x} + 3 x y = ln (x)

x y = cot (x y)