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

The integral of tan(x)sec^3(x) is 1/3 sec^3(x)+C

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

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

\frac{1}{3} sec^{3} (x) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{3} d u

= \int \frac{1}{3} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{3} u

Substitute back

u = sec^{3} (x)

= \frac{1}{3} sec^{3} (x)

Add a constant to the solution

= \frac{1}{3} sec^{3} (x) + C

\int \frac{x}{x + d} d x

\frac{\partial}{\partial x} (x^{3} - 2 x y + y^{2} + 3)

y^{^{'''}} = 0

\frac{4}{5 s}

What is the integral of tan(x)sec^3(x) ?
The integral of tan(x)sec^3(x) is 1/3 sec^3(x)+C