What is the solution for f^'(x)=3e^x+7sec^2(x) ?

The solution for f^'(x)=3e^x+7sec^2(x) is f(x)=3e^x+7tan(x)+c_{1}

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f^'(x)=3e^x+7sec^2(x)

f^{^{'}} (x) = 3 e^{x} + 7 sec^{2} (x)

f (x) = 3 e^{x} + 7 tan (x) + c_{1}

Solution steps

f^{'} (x) = 3 e^{x} + 7 sec^{2} (x)

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (x) = \int 3 e^{x} + 7 sec^{2} (x) d x

\int 3 e^{x} + 7 sec^{2} (x) d x = 3 e^{x} + 7 tan (x) + c_{1}

f (x) = 3 e^{x} + 7 tan (x) + c_{1}

2 y^{^{''}} + y^{^{'}} - y = x + 5

(x + y)^{2} d x + (2 x y + x^{2} - 8) d y = 0, y (1) = 1

\frac{d}{d x} (ln (\frac{x - 2}{x + 2}))

3 y^{^{''}} - 10 y^{^{'}} + 3 y = 0, y (0) = - 5, y^{^{'}} (0) = - 1

\int_{0}^{π} sin^{2} (x) cos (x) d x

What is the solution for f^'(x)=3e^x+7sec^2(x) ?
The solution for f^'(x)=3e^x+7sec^2(x) is f(x)=3e^x+7tan(x)+c_{1}