What is the integral of (4x^3-2sec^2(x)) ?

The integral of (4x^3-2sec^2(x)) is x^4-2tan(x)+C

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integral of (4x^3-2sec^2(x))

\int (4 x^{3} - 2 sec^{2} (x)) d x

x^{4} - 2 tan (x) + C

Solution steps

\int 4 x^{3} - 2 sec^{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 4 x^{3} d x - \int 2 sec^{2} (x) d x

\int 4 x^{3} d x = x^{4}

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

= x^{4} - 2 tan (x)

Add a constant to the solution

= x^{4} - 2 tan (x) + C

\frac{\partial}{\partial x} (9 x y - x^{3} - y^{3} - 6)

\int \frac{sin ( 8 x )}{1 + cos ^{2} ( 8 x )} d x

\frac{d}{d x} (\frac{x + 1}{x})

10

\frac{\partial}{\partial y} (ln (3 x + 5 y))

What is the integral of (4x^3-2sec^2(x)) ?
The integral of (4x^3-2sec^2(x)) is x^4-2tan(x)+C