Evaluate x +2 ( x ^ 2 +3 x +3 ) x +1 dx
Mathematics · JEE Main · NTA Exams — Integral Calculus
Evaluate \(\int \frac{\mathrm{x}+2}{\left(\mathrm{x}^{2}+3 \mathrm{x}+3\right) \sqrt{\mathrm{x}+1}} \mathrm{dx}\)
- \[\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{x}{\sqrt{3(x+1)}}\right)+c\]
- \[\tan ^{-1}\left(\frac{x}{\sqrt{3(x+1)}}\right)+c\]
- \[\frac{\sqrt{3}}{2} \tan ^{-1}\left(\frac{x}{\sqrt{3(x+1)}}\right)+c\]
- \(\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{\mathrm{x}}{3(\mathrm{x}+1)}\right)+\mathrm{c}\)
Answer
(A) 2 3 ^ -1 ( x 3(x+1) )+c
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Let f be a positive function. Let A_ 1 = _ 1-k ^ k x f[x(1-x)] d x and A_ 2 = _ 1-k ^ k f[x(1-x)] d x , where…
- ( x +1)- x x ( x +1) d x is equal to
- _ x 0^ + 1 x^ 3 _ 0 ^ x^ 2 t d t is equal to
- Evaluate _ 0 ^ 2 x 1+ ^ 2 x d x .
- If [ ] denotes the greatest integer function, then the integral _ 0 ^ [ x] d x is equal to:
- The value of _ 0 ^ [x] z^ x z^ [x] d x is, where [ ∙ ] denotes the greatest integer function.
- The value of _ 0 ^ 0 [ ^ -1 x ] d x is
- If . |_ n = _ 0 ^ / 4 ^ n x ^ 2 x d x, then . |_ 1 , . |_ 2 , . |_ 3 are in
More Integral Calculus questions · Browse all practice questions