Help solving another integral \(\displaystyle\int{\left({2}{x}^{{2}}+{4}{x}-{2}\right)}^{{-{\frac{{{3}}}{{{2}}}}}}\ {\left.{d}{x}\right.}\)

Marzadri9lyy

Marzadri9lyy

Answered question

2022-03-26

Help solving another integral
(2x2+4x2)32 dx

Answer & Explanation

Alejandra Hanna

Alejandra Hanna

Beginner2022-03-27Added 10 answers

(2x2+4x2)=2(x2+2x+1)4=2(x+1)24. Now subsitute x+1=2sec{t}. Then you have  dx =2sec{t}tan{t}  dt . Now,
2[(x+1)22]=2[2(sec2{t}1)]=4(sec2{t}1)
Now what will you get if you power them by 32. You will get 
432[tan2{t}]32=8tan3{t}
And try to evaluate the integral. Simplyfying you should get
1(2x2+4x-2)-32 dx=28sect·tanttan3t
=28costsin2t dt 

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