alleryStart learning →After completing the square, how does 1/(x^2 + 2x + 5) integrate?
A(1/2) tan^-1(x + 1) + c
B(1/4) log|x^2+2x+5| + c
Ctan^-1(x + 1) + c
D(1/2) tan^-1((x+1)/2) + c
Answer & Solution
Correct answer: D. (1/2) tan^-1((x+1)/2) + c
Completing the square gives (x+1)^2 + 4, so the integral is (1/2) tan^-1((x+1)/2).
Keep practising Indefinite Integration
Browse all Indefinite Integration questions for MHT-CET, or explore more Mathematics topics.
Related questions
Which method suits (3x+1)/((x-1)(x+2)) when integrating?Which method finds the antiderivative of x cos x most easily?For x^2 log x by parts, which function is taken first?Dividing first, what is the integral of (x^2 + 1)/(x^2 - 1)?Factorising the quadratic x^2 - 5x + 6, what is the primitive of its reciprocal?Which is the partial fraction form for 1/((x-1)^2 (x+2))?Let 1/((x-a)(x-b)) = A/(x-a) + B/(x-b). Then A equals what?Splitting 1/(x(x+1)) into two fractions, what is its antiderivative?