vomiderawo
2021-11-22
Answered

Evaluate the indefinite integral:

$\int {\mathrm{sec}}^{2}x{\mathrm{tan}}^{4}xdx$

You can still ask an expert for help

Symbee

Answered 2021-11-23
Author has **17** answers

Step 1

Evaluate the indefinite integral.

$\int {\mathrm{sec}}^{2}x{\mathrm{tan}}^{4}xdx$

Let$\mathrm{tan}\left(x\right)=t$

${\mathrm{sec}}^{2}\left(x\right)dx=dt$

Step 2

$\int {\mathrm{sec}}^{2}\left(x\right){\mathrm{tan}}^{4}\left(x\right)dx=\int {t}^{4}dt$

$=\frac{{t}^{5}}{5}+c$

$=\frac{{\mathrm{tan}}^{5}\left(x\right)}{5}+c$

Evaluate the indefinite integral.

Let

Step 2

Mary Ramirez

Answered 2021-11-24
Author has **19** answers

Step 1: Use Integration by Substitution.

Let$u=\mathrm{tan}x,du={\mathrm{sec}}^{2}xdx$

Step 2: Using u and du above, rewrite$\int {\mathrm{sec}}^{2}x{\mathrm{tan}}^{4}xdx$ .

$\int {u}^{4}du$

Step 3: Use Power Rule:$\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+C$ .

$\frac{{u}^{5}}{5}$

Step 4: Substitute$u=\mathrm{tan}x$ back into the original integral.

$\frac{{\mathrm{tan}}^{5}x}{5}$

Step 5: Add constant.

$\frac{{\mathrm{tan}}^{5}x}{5}+C$

Let

Step 2: Using u and du above, rewrite

Step 3: Use Power Rule:

Step 4: Substitute

Step 5: Add constant.

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