If d/dx (F(x)) = 1/(eˣ + 1), then find F(x) given that F(0) = log(1/2).

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

Indefinite Integral and Its Properties, Integration by Partial Fractions, Particular Solution of a Differential Equation | PadhAiPro

Question

TextIndefinite Integral and Its PropertiesIntegration by Partial FractionsParticular Solution of a Differential Equation

Find : ∫ x²/((x² + 4)(x² + 9)) dx

Evaluate : ∫₁³ (|x – 1| + |x – 2| + |x – 3|) dx

Properties of Definite Integrals

Find the particular solution of the differential equation given by x² (dy/dx) – xy = x² cos² (y/(2x)), given that when x = 1, y = π/2.

Find : ∫ (e⁴ˣ – 1)/(e⁴ˣ + 1) dx

Evaluate : ∫ from 0 to π/2 sin 2x cos 3x dx

Given d/dx F(x) = 1/√(2x – x²) and F(1) = 0, find F(x).