What is the integral of ((1+cos^2(x)))/(cos^2(x)) ?

The integral of ((1+cos^2(x)))/(cos^2(x)) is tan(x)+x+C

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integral of ((1+cos^2(x)))/(cos^2(x))

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

tan (x) + x + C

Solution steps

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

Expand

\frac{1 + cos ^{2} ( x )}{cos ^{2} ( x )} : \frac{1}{cos ^{2} ( x )} + 1

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

\int \frac{1}{cos ^{2} ( x )} d x = tan (x)

\int 1 d x = x

= tan (x) + x

Add a constant to the solution

= tan (x) + x + C

\frac{6 x ^{2} + 8 x + 8 x}{x}

\frac{x ^{2}}{y ^{2} - 2} y^{^{'}} = \frac{1}{2 y}, y (1) = 3

\int \frac{2 x ^{4} + 3 x ^{2} - 2 x ^{- 3}}{x ^{2}} d x

n = 1 \sum \infty \frac{1}{6 n + 5}

y^{^{'}} = \frac{( y ^{2} + 2 x y )}{x ^{2}}

What is the integral of ((1+cos^2(x)))/(cos^2(x)) ?
The integral of ((1+cos^2(x)))/(cos^2(x)) is tan(x)+x+C