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

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

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

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

- tan (cos (x)) + C

Solution steps

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

Apply u-substitution

: \int - sec^{2} (u) d u

= \int - sec^{2} (u) d u

Take the constant out:

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

= - \int sec^{2} (u) d u

Use the common integral:

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

= - tan (u)

Substitute back

u = cos (x)

= - tan (cos (x))

Add a constant to the solution

= - tan (cos (x)) + C

f (x) = 2 x^{2}, at x = 5

\int 7 cos^{2} (x) sin (2 x) d x

\int t^{2} cos (n t) d t

\int \frac{- x}{x} d x

s \to 0 lim (s \cdot \frac{k}{s \cdot ( \frac{s}{5} + 1 ) \cdot ( \frac{s}{50} + 1 )})

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