What is the integral of-7sec^2(x) ?

The integral of-7sec^2(x) is -7tan(x)+C

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integral of-7sec^2(x)

\int - 7 sec^{2} (x) d x

- 7 tan (x) + C

Solution steps

\int - 7 sec^{2} (x) d x

Take the constant out:

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

= - 7 \cdot \int sec^{2} (x) d x

Use the common integral:

\int sec^{2} (x) d x = tan (x)

= - 7 tan (x)

Add a constant to the solution

= - 7 tan (x) + C

y^{^{'}} + 5 y = 0, y (0) = 2

\int (5 x^{2} - 5 x + 4 tan (x)) d x

\frac{d}{d x} (20 x (2 x^{2} + 7)^{4})

2 + 6 x^{2} - 2 x^{3}