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

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

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integral of cos^3(x)tan^2(x)

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

\frac{sin ^{3} ( x )}{3} + C

Solution steps

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

Rewrite using trig identities

= \int sin^{2} (x) cos (x) d x

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = sin (x)

= \frac{sin ^{3} ( x )}{3}

Add a constant to the solution

= \frac{sin ^{3} ( x )}{3} + C

f (x) = \frac{4}{1 + x ^{2}}, at x = 1

x \to \frac{π}{2} - lim (e^{s e c (x)})

\int \frac{e t}{t} d t

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

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