What is the integral of (x^5-sec^2(x)) ?

The integral of (x^5-sec^2(x)) is (x^6)/6-tan(x)+C

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integral of (x^5-sec^2(x))

\int (x^{5} - sec^{2} (x)) d x

\frac{x ^{6}}{6} - tan (x) + C

Solution steps

\int x^{5} - 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^{5} d x - \int sec^{2} (x) d x

\int x^{5} d x = \frac{x ^{6}}{6}

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

= \frac{x ^{6}}{6} - tan (x)

Add a constant to the solution

= \frac{x ^{6}}{6} - tan (x) + C

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

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\int (3 x^{2} + \frac{9}{2 x ^{3}}) d x

\int \frac{2}{3 x + 2} d x

What is the integral of (x^5-sec^2(x)) ?
The integral of (x^5-sec^2(x)) is (x^6)/6-tan(x)+C