# Evaluate the indefinite integral. \int \sec^{2}0\tan^{2}0d0

Evaluate the indefinite integral.
$\int {\mathrm{sec}}^{2}0{\mathrm{tan}}^{2}0d0$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Cristiano Sears
Step 1
Calculate the indefinite integral.
$\int {\mathrm{sec}}^{2}0{\mathrm{tan}}^{2}0d0$
Consider,
$u=\mathrm{tan}0$
$du={\mathrm{sec}}^{2}0d0$
Step 2
Substitution the value u and du.
$\int {\mathrm{sec}}^{2}0\left({\mathrm{tan}}^{2}0\right)d0$
$⇒\int {u}^{2}du$
Apply power rule: $\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}$
$⇒\frac{{u}^{2+1}}{2+1}$
$⇒\frac{{u}^{3}}{3}$
We know that, $u=\mathrm{tan}0$.
$⇒\frac{{\mathrm{tan}}^{3}0}{3}+c$; c=constant.