Exams › JEE Main › Maths

Evaluate the integral ∫ e^(tan⁻¹x) (1+x+x²)/(1+x²) dx.

1. x e^(tan⁻¹x) + C
2. tan⁻¹x + C
3. e^(tan⁻¹x) + 2x + C
4. None of these

Correct answer: x e^(tan⁻¹x) + C

Solution

The integral evaluates to the product of the variable x and the exponential function of the inverse tangent, indicating that the function's growth is influenced by both x and the exponential term, which is consistent with the result of option A.

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 →