Exams › JEE Main › Maths

Find the indefinite integral of 8/((x + 2)(x² + 4)) with respect to x.

1. ln|x + 2| − 1/2 ln(x² + 4) + tan^(-1)(x/2) + C
2. ln|x + 2| − 1/2 ln(x² + 4) + sin^(-1)(x/2) + C
3. ln|x + 2| − 1/2 ln(x² + 4) + cos^(-1)(x/2) + C
4. ln|x + 2| − 1/2 ln(x³ + 4) + tan^(-1)(x/2) + C

Correct answer: ln|x + 2| − 1/2 ln(x² + 4) + tan^(-1)(x/2) + C

Solution

The correct option accurately combines the natural logarithm of the linear term and the inverse tangent function, which arises from the integration of the rational function involving a quadratic term, ensuring the proper application of integration techniques such as partial fraction decomposition.

Related JEE Main Maths questions

• For the function y = a²/x + b²/(a - x), where a > 0 and b > 0, the least value of y for x in the interval (0, a) is:
• Let f(x)=∫ from 2x to sin x of cos(t³) dt. Then the value of f''(x) is
• Evaluate the integral ∫_(√(ln 3))^(√(ln 2)) (xsin(x²))/(sin(x²)+sin(ln 6-x²)) dx.
• Evaluate the integral ∫ (e^x (1+xⁿ⁻¹-xⁿ))/((1-xⁿ)√(1-x²ⁿ)) dx.
• Let J = ∫ from 0 to 1 of (cos x)/√x dx and K = ∫ from 0 to 1 of (sin x)/√x dx. Which of the following statements is correct?
• A curve passes through the point (0,1) and satisfies y = ∫ x² e^(x³) dx. If this curve is expressed as x = f(y), then f(y) equals

⚔️ Practice JEE Main Maths free + battle 1v1 →