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

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

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

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

\frac{x ^{3}}{3} - tan (x) + C

Solution steps

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

\int x^{2} d x = \frac{x ^{3}}{3}

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

= \frac{x ^{3}}{3} - tan (x)

Add a constant to the solution

= \frac{x ^{3}}{3} - tan (x) + C

x \to \infty lim (\frac{1 - e - x}{1 + e ^{- x}})

\frac{e ^{2 x}}{x + 1}

n = 6 \sum \infty \frac{1}{n ^{3}}

\int \frac{1}{8 x} d x

\frac{d y}{d x} = \frac{x ^{6} - 2 y}{x}

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