1. Integral x/ (x+4) ^(1/2) dx
2. Integral [e^(2x) - 1] / [e^(2x) + 1] dx
3. Integral (x)^5 [x^3 -1]^(1/3) dx
4. Integral sin[arctan(x)] / (1+x^2) dx
2007-03-18 03:06:43 · 3 answers · asked by fm02 2 in Science & Mathematics ➔ Mathematics
1) x= 2tany
dx/dy= 2sec^2y
dx=2sec^2y dy
√(4tan^2y)+4= √(4sec^2y)=2secy
integrate (2tany*sec^2y)/*(2secy) dy
=integrate tanysecy dy
= sec y +c
replace y w/ x
integral= sec(tan^(-1)x) +c ==> Ans
4) u= arctanx
du/dx= 1/(1+x^2)
du=dx/(1+x^2)
therefore integral:
integrate sinu du =cosu+c
substitute back:
cos(arctanx) +c ==> Ans
2007-03-18 03:23:15 · answer #1 · answered by Maths Rocks 4 · 0⤊ 0⤋
1) x= 2tany
dx/dy= 2sec^2y
dx=2sec^2y dy
â(4tan^2y)+4= â(4sec^2y)=2secy
integrate (2tany*sec^2y)/*(2secy) dy
=integrate tanysecy dy
= sec y +c
replace y w/ x
integral= sec(tan^(-1)x) +c ==> Ans
4) u= arctanx
du/dx= 1/(1+x^2)
du=dx/(1+x^2)
therefore integral:
integrate sinu du =cosu+c
substitute back:
cos(arctanx) +c ==> Ans
2007-03-20 10:40:25 · answer #2 · answered by pa r 1 · 0⤊ 1⤋
dude, just take the antiderivative and evaluate
2007-03-18 10:13:18 · answer #3 · answered by sur2124 4 · 0⤊ 2⤋