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

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

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

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

sec (t) + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{u ^{2}} d u

= \int - \frac{1}{u ^{2}} d u

Take the constant out:

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

= - \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - (- \frac{1}{u})

Substitute back

u = cos (t)

= - (- \frac{1}{cos ( t )})

Simplify

- (- \frac{1}{cos ( t )}) : sec (t)

= sec (t)

Add a constant to the solution

= sec (t) + C

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\frac{\partial}{\partial x} (x^{2} + 4 x y + y^{6} - 8)

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