What is the integral of ((e^{tan(x)}))/(cos^2(x)) ?

The integral of ((e^{tan(x)}))/(cos^2(x)) is e^{tan(x)}+C

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integral of ((e^{tan(x)}))/(cos^2(x))

\int \frac{( e ^{t a n (x)} )}{cos ^{2} ( x )} d x

e^{t a n (x)} + C

Solution steps

\int \frac{e ^{t a n (x)}}{cos ^{2} ( x )} d x

Rewrite using trig identities

= \int \frac{e ^{t a n (x)}}{1 - sin ^{2} ( x )} d x

Apply Integration By Parts

: e^{t a n (x)} tan (x) - \int e^{t a n (x)} sec^{2} (x) tan (x) d x

= e^{t a n (x)} tan (x) - \int e^{t a n (x)} sec^{2} (x) tan (x) d x

\int e^{t a n (x)} sec^{2} (x) tan (x) d x = tan (x) e^{t a n (x)} - e^{t a n (x)}

= e^{t a n (x)} tan (x) - (tan (x) e^{t a n (x)} - e^{t a n (x)})

Simplify

e^{t a n (x)} tan (x) - (tan (x) e^{t a n (x)} - e^{t a n (x)}) : e^{t a n (x)}

= e^{t a n (x)}

Add a constant to the solution

= e^{t a n (x)} + C

y^{^{''}} + 5 y^{^{'}} + 2 y = 7

y = 2 x^{3}, (2, 16)

\int \frac{1}{x x + 1} d x

y = (\frac{x}{1 + x})^{5}

\frac{d}{d x} (2 x \cdot e^{x^{2}})

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