What is the integral of 5sec^2(x)e^{tan(x)} ?

The integral of 5sec^2(x)e^{tan(x)} is 5e^{tan(x)}+C

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integral of 5sec^2(x)e^{tan(x)}

\int 5 sec^{2} (x) e^{t a n (x)} d x

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

Solution steps

\int 5 sec^{2} (x) e^{t a n (x)} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int sec^{2} (x) e^{t a n (x)} d x

Apply u-substitution

= 5 \cdot \int e^{u} d u

Use the common integral:

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

= 5 e^{u}

Substitute back

u = tan (x)

= 5 e^{t a n (x)}

Add a constant to the solution

= 5 e^{t a n (x)} + C

What is the integral of 5sec^2(x)e^{tan(x)} ?
The integral of 5sec^2(x)e^{tan(x)} is 5e^{tan(x)}+C