Integration by parts

[Maddie]

Who can help me solve this question

1+ tan²x =sec²x.
∫sec³ x dx using integration by parts

 

[Deleted member 4993]

Who can help me solve this question

1+ tan²x =sec²x.
∫sec³ x dx using integration by parts

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this assignment.

By the way - it is a "nasty" one!

 

[Maddie]

1+ tan²x =sec²x.
∫sec³ x dx using integration by parts

U= sec x

du=secx tanx dx

dv=sec²x dx

v=tanx

So here is what I did,

∫sec³x dx

= ∫sec²x * sec x dx

= secx tanx * ∫secx tan²x dx


And I'm stuck here

 

[Deleted member 4993]

1+ tan²x =sec²x.
∫sec³ x dx using integration by parts ........U= sec x du=secx tanx dv=sec²x v=tanx .......So here is what I did,

∫sec³x = ∫sec²x X sec x...........= secx tanx x ∫secx tan²x dx ...........incorrect ...........And I'm stuck here

The formula for integration by parts Is

\(\displaystyle \int u(x) \ d[v(x)] = u(x) * v(x) - \int v(x) \ d[u(x)]\)

Carefully check signs..........................edited

 

[Steven G]

First you really need to separate your equals possible by using commas!!
u= sec x, du=secx tanxdx, dv=sec²x, v=tanx

Do NOT use x as a variable and X for the multiplication symbol. Use * for multiplication.

You made a little mistake with the formula. Replace X with -
After you fix the little mistake you made in that last integral you should substitute tan^2(x) with sec^2(x) - 1

Post back with your work.

 

[Maddie]

The formula for integration by parts Is

\(\displaystyle \int u(x) \ d[v(x)] = u(x) * v(x) - \int v(x) \ d[u(x)]\)

What did you assign as u(x) and v(x)?

The formula for integration by parts Is

\(\displaystyle \int u(x) \ d[v(x)] = u(x) * v(x) - \int v(x) \ d[u(x)]\)

First you really need to separate your equals possible by using commas!!
u= sec x, du=secx tanxdx, dv=sec²x, v=tanx

Do NOT use x as a variable and X for the multiplication symbol. Use * for multiplication.

You made a little mistake with the formula. Replace X with -
After you fix the little mistake you made in that last integral you should substitute tan^2(x) with sec^2(x) - 1

Post back with your work.

What did you assign as u(x) and v(x)?

U(

First you really need to separate your equals possible by using commas!!
u= sec x, du=secx tanxdx, dv=sec²x, v=tanx

Do NOT use x as a variable and X for the multiplication symbol. Use * for multiplication.

You made a little mistake with the formula. Replace X with -
After you fix the little mistake you made in that last integral you should substitute tan^2(x) with sec^2(x) - 1

Post back with your work.

1+ tan²x =sec²x.
∫sec³ x dx using integration by parts

U= sec x, du=secxtanx dx, dv=sec²x , v=tanx

So here is what I did,

∫sec³x = ∫sec²x * sec x
= secx tanx -∫secx tan²x dx
=secx tanx-∫secx*sec²x-1 dx (?)

 

[Steven G]

Ah, you are getting ∫sec³xdx! So bring it to the other side of the equal sign.

 

[Deleted member 4993]

U(

1+ tan²x =sec²x.
∫sec³ x dx using integration by parts

U= sec x, du=secxtanx dx, dv=sec²x , v=tanx

So here is what I did,

∫sec³x dx = ∫sec²x * sec x
= secx tanx -∫secx tan²x dx
=secx tanx-∫secx*(sec²x-1) dx (?)

∫sec³x dx = secx tanx - ∫secx*(sec²x-1) dx

2 * ∫sec³x dx = secx * tanx + ∫secx dx

continue.......