What is the integral of (sin(θ))/(cos^3(θ)) ?

The integral of (sin(θ))/(cos^3(θ)) is (tan^2(θ))/2+C

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integral of (sin(θ))/(cos^3(θ))

\int \frac{sin ( θ )}{cos ^{3} ( θ )} d θ

\frac{tan ^{2} ( θ )}{2} + C

Solution steps

\int \frac{sin ( θ )}{cos ^{3} ( θ )} d θ

Rewrite using trig identities

= \int tan (θ) sec^{2} (θ) d θ

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = tan (θ)

= \frac{tan ^{2} ( θ )}{2}

Add a constant to the solution

= \frac{tan ^{2} ( θ )}{2} + C

\frac{d}{d x} ((3 x^{2} - 2)^{3})

\frac{d y}{d x} = 6 x (x - 3)

\int \frac{x + 2}{( x ^{2} + 4 x ) ^{2}} d x

4 x - 8

9 - 4 x, at x = - 1

What is the integral of (sin(θ))/(cos^3(θ)) ?
The integral of (sin(θ))/(cos^3(θ)) is (tan^2(θ))/2+C