What is the integral of sec(a)xtan(a)x ?

The integral of sec(a)xtan(a)x is 1/3 x^3sec(a)tan(a)+C

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integral of sec(a)xtan(a)x

\int sec (a) x tan (a) x d x

\frac{1}{3} x^{3} sec (a) tan (a) + C

Solution steps

\int sec (a) x tan (a) x d x

Take the constant out:

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

= sec (a) tan (a) \cdot \int xx d x

Simplify

xx : x^{2}

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= sec (a) tan (a) \frac{x ^{3}}{3}

Simplify

sec (a) tan (a) \frac{x ^{3}}{3} : \frac{1}{3} x^{3} sec (a) tan (a)

= \frac{1}{3} x^{3} sec (a) tan (a)

Add a constant to the solution

= \frac{1}{3} x^{3} sec (a) tan (a) + C

\frac{d y}{d x} + 2 y = e^{3 x} y^{2}

\int \frac{1}{1 + 1 - x ^{2}} d x

\int \frac{1}{( x ^{2} + 1 ) ^{3}} d x

\int sec^{2} (x) (1 + tan (x)) d x

What is the integral of sec(a)xtan(a)x ?
The integral of sec(a)xtan(a)x is 1/3 x^3sec(a)tan(a)+C