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

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

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

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

- tan (cos (t)) + C

Solution steps

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

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 (t)

= - tan (cos (t))

Add a constant to the solution

= - tan (cos (t)) + C

\int_{3}^{0} (5 x - x^{3}) d x

y^{^{'}} = \frac{3 y ^{2} + 3}{2 x y}

\frac{d y}{d x} = 6 x y

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

\frac{d y}{d x} = 1 0^{x + y}

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