What is the integral of 5tan(x)sec^3(x) ?

The integral of 5tan(x)sec^3(x) is 5/3 sec^3(x)+C

integral of 5tan(x)sec^3(x)

\int 5 tan (x) sec^{3} (x) d x

\frac{5}{3} sec^{3} (x) + C

Solution steps

\int 5 tan (x) sec^{3} (x) d x

Take the constant out:

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

= 5 \cdot \int tan (x) sec^{3} (x) d x

Apply u-substitution

= 5 \cdot \int \frac{1}{3} d u

Integral of a constant:

\int a d x = a x

= 5 \cdot \frac{1}{3} u

Substitute back

u = sec^{3} (x)

= 5 \cdot \frac{1}{3} sec^{3} (x)

Simplify

5 \cdot \frac{1}{3} sec^{3} (x) : \frac{5}{3} sec^{3} (x)

= \frac{5}{3} sec^{3} (x)

Add a constant to the solution

= \frac{5}{3} sec^{3} (x) + C

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

\int ln (1 + y) d y

d er i v a t i v e y = ln (x + 3)

y^{^{''}} + 9 y = - sin (3 t)

a re a y = 2 x^{3} + 3 x^{2} - 4 x, y = x^{2}

What is the integral of 5tan(x)sec^3(x) ?
The integral of 5tan(x)sec^3(x) is 5/3 sec^3(x)+C