What is the integral of-e^x-7/(cos^2(x)) ?

The integral of-e^x-7/(cos^2(x)) is -e^x-7tan(x)+C

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integral of-e^x-7/(cos^2(x))

\int - e^{x} - \frac{7}{cos ^{2} ( x )} d x

- e^{x} - 7 tan (x) + C

Solution steps

\int - e^{x} - \frac{7}{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 e^{x} d x - \int \frac{7}{cos ^{2} ( x )} d x

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

\int \frac{7}{cos ^{2} ( x )} d x = 7 tan (x)

= - e^{x} - 7 tan (x)

Add a constant to the solution

= - e^{x} - 7 tan (x) + C

What is the integral of-e^x-7/(cos^2(x)) ?
The integral of-e^x-7/(cos^2(x)) is -e^x-7tan(x)+C