What is the integral of xsec(8)x^2tan(8)x^2 ?

The integral of xsec(8)x^2tan(8)x^2 is 1/6 sec(8)tan(8)x^6+C

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integral of xsec(8)x^2tan(8)x^2

\int x sec (8) x^{2} tan (8) x^{2} d x

\frac{1}{6} sec (8) tan (8) x^{6} + C

Solution steps

\int x sec (8) x^{2} tan (8) x^{2} d x

Take the constant out:

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

= sec (8) tan (8) \cdot \int x x^{2} x^{2} d x

Simplify

x x^{2} x^{2} : x^{5}

= sec (8) tan (8) \cdot \int x^{5} d x

Apply the Power Rule

: \frac{x ^{6}}{6}

= sec (8) tan (8) \frac{x ^{6}}{6}

Simplify

sec (8) tan (8) \frac{x ^{6}}{6} : \frac{1}{6} sec (8) tan (8) x^{6}

= \frac{1}{6} sec (8) tan (8) x^{6}

Add a constant to the solution

= \frac{1}{6} sec (8) tan (8) x^{6} + C

\frac{d}{d x} (tan (3 x))

\frac{d}{d x} (\frac{( 8 x )}{x ^{2} + 4})

x \to 0 lim (\frac{1 - e ^{x}}{x})

f (x) = 1 - 3 x^{[2]}, at x = 0

\int \frac{3}{y} d y

What is the integral of xsec(8)x^2tan(8)x^2 ?
The integral of xsec(8)x^2tan(8)x^2 is 1/6 sec(8)tan(8)x^6+C