What is the integral of cos^4(x)tan^3(x) ?

The integral of cos^4(x)tan^3(x) is (sin^4(x))/4+C

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integral of cos^4(x)tan^3(x)

\int cos^{4} (x) tan^{3} (x) d x

\frac{sin ^{4} ( x )}{4} + C

Solution steps

\int cos^{4} (x) tan^{3} (x) d x

Rewrite using trig identities

= \int sin^{3} (x) cos (x) d x

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 = sin (x)

= \frac{sin ^{4} ( x )}{4}

Add a constant to the solution

= \frac{sin ^{4} ( x )}{4} + C

\frac{1}{x ^{2}}, x, 8 x

\int_{0}^{1} \frac{1}{( x - 2 ) ^{2}} d x

x \to 0 lim (\frac{e ^{x} cos ( x )}{4})

\frac{d}{d x} (\frac{e ^{x}}{4 + e ^{x}})

\frac{d}{d x} (\frac{x ^{3} - 5 x ^{2} - 36 x}{x ^{2} + 4 x})

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