What is the integral of tan(θ)sec(θ) ?

The integral of tan(θ)sec(θ) is sec(θ)+C

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integral of tan(θ)sec(θ)

\int tan (θ) sec (θ) d θ

sec (θ) + C

Solution steps

\int tan (θ) sec (θ) d θ

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 (θ)

= 1 \cdot sec (θ)

Simplify

= sec (θ)

Add a constant to the solution

= sec (θ) + C

y^{^{'}} = e^{4 x + y}

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

x \to 2 - lim (\frac{1}{( x - 2 ) ^{2}})

\frac{d y}{d x} = 4 x - 5 y

2 x^{2} + 5 x + 1