Evaluate the integral.

$\int x\mathrm{sec}x\mathrm{tan}xdx$

Lennie Carroll
2021-11-09
Answered

Evaluate the integral.

$\int x\mathrm{sec}x\mathrm{tan}xdx$

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SabadisO

Answered 2021-11-10
Author has **108** answers

Step 1

u=x

du=dx

$dv=\mathrm{sec}x\cdot \mathrm{tan}x\cdot dx$

$v=\int \mathrm{sec}x\cdot \mathrm{tan}x\cdot dx$

$v=\mathrm{sec}x$

Step 2

Then we integrate by parts

$\int x\cdot \mathrm{sec}x\cdot \mathrm{tan}x\cdot dx$

$=\int u\cdot dv$

$=uv-\int v\cdot du$

$=x\cdot \mathrm{sec}x-\int \mathrm{sec}xdx$

$=x\cdot \mathrm{sec}x-\mathrm{ln}|\mathrm{sec}x+\mathrm{tan}x|+C$

Answer:$x\cdot \mathrm{sec}x-\mathrm{ln}|\mathrm{sec}x+\mathrm{tan}x|+C$

C=integrating constant

u=x

du=dx

Step 2

Then we integrate by parts

Answer:

C=integrating constant

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