What is the integral of (tan^3(θ))/(cos^2(θ)) ?

The integral of (tan^3(θ))/(cos^2(θ)) is (tan^4(θ))/4+C

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integral of (tan^3(θ))/(cos^2(θ))

\int \frac{tan ^{3} ( θ )}{cos ^{2} ( θ )} d θ

\frac{tan ^{4} ( θ )}{4} + C

Solution steps

\int \frac{tan ^{3} ( θ )}{cos ^{2} ( θ )} d θ

Rewrite using trig identities

= \int (1 + tan^{2} (θ)) tan^{3} (θ) d θ

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = tan (θ)

= \frac{tan ^{4} ( θ )}{4}

Add a constant to the solution

= \frac{tan ^{4} ( θ )}{4} + C

f (x) = x^{2} - 3 x + 2, at x = 1

(x + 9) (9 x + 7)

\int x 7 - x^{2} d x

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

f (x) = cos (7 x)

What is the integral of (tan^3(θ))/(cos^2(θ)) ?
The integral of (tan^3(θ))/(cos^2(θ)) is (tan^4(θ))/4+C