What is the integral of (cos^3(x)+4)/(cos^2(x)) ?

The integral of (cos^3(x)+4)/(cos^2(x)) is sin(x)+4tan(x)+C

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integral of (cos^3(x)+4)/(cos^2(x))

\int \frac{cos ^{3} ( x ) + 4}{cos ^{2} ( x )} d x

sin (x) + 4 tan (x) + C

Solution steps

\int \frac{cos ^{3} ( x ) + 4}{cos ^{2} ( x )} d x

Expand

\frac{cos ^{3} ( x ) + 4}{cos ^{2} ( x )} : cos (x) + \frac{4}{cos ^{2} ( x )}

= \int cos (x) + \frac{4}{cos ^{2} ( x )} 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 cos (x) d x + \int \frac{4}{cos ^{2} ( x )} d x

\int cos (x) d x = sin (x)

\int \frac{4}{cos ^{2} ( x )} d x = 4 tan (x)

= sin (x) + 4 tan (x)

Add a constant to the solution

= sin (x) + 4 tan (x) + C

\int 3 sin^{2} (x) cos^{2} (x) d x

\frac{\partial}{\partial y} (\frac{- x - 7 y}{y ^{2} + 2 x ^{2}})

\int \frac{1}{x ( 1 + x ) ^{2}} d x

x \to 4 lim (\frac{- x + 4}{x})

\frac{d}{d x} (e^{2 x} (x - 4) (x + 6))

What is the integral of (cos^3(x)+4)/(cos^2(x)) ?
The integral of (cos^3(x)+4)/(cos^2(x)) is sin(x)+4tan(x)+C