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

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

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integral of (sin(t))/(cos^3(t))

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

\frac{tan ^{2} ( t )}{2} + C

Solution steps

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

Rewrite using trig identities

= \int tan (t) sec^{2} (t) d t

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 (t)

= \frac{tan ^{2} ( t )}{2}

Add a constant to the solution

= \frac{tan ^{2} ( t )}{2} + C

x \to - 3 lim (1)

\frac{d}{d x} (x^{3} \cdot cos (x))

\frac{d}{d x} (3 x^{\frac{2}{3}} - 6 x^{\frac{1}{3}} + x^{- \frac{1}{3}})

\frac{d}{d x} (\frac{1}{2} x sin (x))

\int 9 t sec^{2} (2 t) d t

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