What is the integral of e^x+2cos(x)-3/(cos^2(x)) ?

The integral of e^x+2cos(x)-3/(cos^2(x)) is e^x+2sin(x)-3tan(x)+C

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integral of e^x+2cos(x)-3/(cos^2(x))

\int e^{x} + 2 cos (x) - \frac{3}{cos ^{2} ( x )} d x

e^{x} + 2 sin (x) - 3 tan (x) + C

Solution steps

\int e^{x} + 2 cos (x) - \frac{3}{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 2 cos (x) d x - \int \frac{3}{cos ^{2} ( x )} d x

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

\int 2 cos (x) d x = 2 sin (x)

\int \frac{3}{cos ^{2} ( x )} d x = 3 tan (x)

= e^{x} + 2 sin (x) - 3 tan (x)

Add a constant to the solution

= e^{x} + 2 sin (x) - 3 tan (x) + C

\frac{\partial}{\partial y} (\frac{3 y}{x ^{2} + y ^{2}})

x \to 0 lim (\frac{cos ( x )}{x - \frac{π}{2}})

\int \frac{2 x ^{2}}{1 - 6 x ^{3}} d x

\frac{\partial}{\partial x} (sin (y) - y sin (x))

f (x) = 3 x^{3} - x^{2} + 2, (1, 4)

What is the integral of e^x+2cos(x)-3/(cos^2(x)) ?
The integral of e^x+2cos(x)-3/(cos^2(x)) is e^x+2sin(x)-3tan(x)+C