Show the steps needed to find the given solutions. ∫arctan⁡c1+x2dx

chezmarylou1i

chezmarylou1i

Answered

2021-12-23

Show the steps needed to find the given solutions.
arctanc1+x2dx

Answer & Explanation

Travis Hicks

Travis Hicks

Expert

2021-12-24Added 29 answers

1) arctan(x)1+x2dx
Let u=arctan(x)
dudx=ddx(arctan(x))
dudx=11+x2dx=du(1+x2)
Substiute dx value in eq. 1
udu(1+x2)(1+x2)=udu=u22+C
Substitute "u" (arctan(x))22+C
Jeffery Autrey

Jeffery Autrey

Expert

2021-12-25Added 35 answers

2) cos2xsinxdx
Let u=cosxdudx=ddx(cosx)
=sinx
Substitute dx "value inequality" dusinx=dx
u3sinxdusinx=u2du=u44+C
Substitute "u" value
=cos4x4+C
karton

karton

Expert

2021-12-30Added 439 answers

3) sec2xtan3xdx
Let u=tanx:⇒dudx=ddx(tanx)
dx=1sec2xdu
Substitute "dx" value in equation
sec2xu2dusec2x=u44+C=tan4(x)4+C

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