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

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

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integral of (tan^2(x))/(sin(x))

\int \frac{tan ^{2} ( x )}{sin ( x )} d x

sec (x) + C

Solution steps

\int \frac{tan ^{2} ( x )}{sin ( x )} d x

Simplify

\frac{tan ^{2} ( x )}{sin ( x )} : sec (x) tan (x)

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

Apply u-substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = sec (x)

= 1 \cdot sec (x)

Simplify

= sec (x)

Add a constant to the solution

= sec (x) + C

\int x^{2} - 2 y d y

\frac{d y}{d x} = 2 x 1 - y^{2}

d y - (y - 1) 2 d x = 0

x \to 5 lim (\frac{∣ 5 - x ∣}{5 - x})

\frac{\partial}{\partial x} (e^{x + 6 y})

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