What is the integral of e^{tan(x)}*sec^2(x) ?

The integral of e^{tan(x)}*sec^2(x) is e^{tan(x)}+C

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integral of e^{tan(x)}*sec^2(x)

\int e^{t a n (x)} \cdot sec^{2} (x) d x

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

Solution steps

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

Apply u-substitution

: \int e^{u} d u

= \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= e^{u}

Substitute back

u = tan (x)

= e^{t a n (x)}

Add a constant to the solution

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

\int_{0}^{π} sin (x) sin (n x) d x

\int \frac{y - 1}{( 4 + y ^{2} ) ^{2}} d y

\int (4 x - 3)^{6} d x

x \to 2 + lim (\frac{x + 3}{x - 2})

f (x) = \frac{6}{x}, at x = 1

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