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

The integral of sec^2(x)sin(x) is sec(x)+C

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

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

sec (x) + C

Solution steps

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

Rewrite using trig identities

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

Apply Integration By Parts

: - sec (x) - \int - 2 sec (x) tan (x) d x

= - sec (x) - \int - 2 sec (x) tan (x) d x

\int - 2 sec (x) tan (x) d x = - 2 sec (x)

= - sec (x) - (- 2 sec (x))

Simplify

= sec (x)

Add a constant to the solution

= sec (x) + C

\int x^{0.5} d x

\int \frac{1}{x ^{3} + 4 x} d x

f (x) = 4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 2 x

f (x) = \frac{2}{x}, at \frac{1}{16}

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

What is the integral of sec^2(x)sin(x) ?
The integral of sec^2(x)sin(x) is sec(x)+C