What is the integral of (sec^4(x)tan(x))/(243) ?

The integral of (sec^4(x)tan(x))/(243) is 1/972 sec^4(x)+C

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integral of (sec^4(x)tan(x))/(243)

\int \frac{sec ^{4} ( x ) tan ( x )}{243} d x

\frac{1}{972} sec^{4} (x) + C

Solution steps

\int \frac{sec ^{4} ( x ) tan ( x )}{243} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{243} \cdot \int sec^{4} (x) tan (x) d x

Apply u-substitution

: \int u^{3} d u

= \frac{1}{243} \cdot \int u^{3} d u

Apply the Power Rule

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

= \frac{1}{243} \cdot \frac{u ^{4}}{4}

Substitute back

u = sec (x)

= \frac{1}{243} \cdot \frac{sec ^{4} ( x )}{4}

Simplify

\frac{1}{243} \cdot \frac{sec ^{4} ( x )}{4} : \frac{1}{972} sec^{4} (x)

= \frac{1}{972} sec^{4} (x)

Add a constant to the solution

= \frac{1}{972} sec^{4} (x) + C

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What is the integral of (sec^4(x)tan(x))/(243) ?
The integral of (sec^4(x)tan(x))/(243) is 1/972 sec^4(x)+C