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

The integral of (sec^2(x)tan^3(x)) is (tan^4(x))/4+C

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

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

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

Solution steps

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

Rewrite using trig identities

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

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

Add a constant to the solution

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

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