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Popular >

integral of tan(θ)

Solution

\int tan (θ) d θ

Solution

- ln ∣ cos (θ) ∣ + C

Solution steps

\int tan (θ) d θ

Rewrite using trig identities

= \int \frac{sin ( θ )}{cos ( θ )} d θ

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = cos (θ)

= - ln ∣ cos (θ) ∣

Add a constant to the solution

= - ln ∣ cos (θ) ∣ + C

Popular Examples

integral of x(x-1)^{10}

\int x (x - 1)^{10} d x

(x^{3} \cdot cos (x))^{^{'}}

y^{1/2}*(dy)/(dx)+y^{3/2}=1

y^{\frac{1}{2}} \cdot \frac{d y}{d x} + y^{\frac{3}{2}} = 1

integral of 1/(3sin^2(x)+5cos^2(x))

\int \frac{1}{3 sin ^{2} ( x ) + 5 cos ^{2} ( x )} d x

derivative of 2sin(x+sin(2x))

\frac{d}{d x} (2 sin (x) + sin (2 x))

Frequently Asked Questions (FAQ)

What is the integral of tan(θ) ?
The integral of tan(θ) is -ln|cos(θ)|+C