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 : ∫ (e⁴ˣ – 1)/(e⁴ˣ + 1) dx

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

Find the particular solution of the differential equation dy/dx = y cot 2x, given that y(π/4) = 2.

Find the particular solution of the differential equation (xe^(y/x) + y) dx = x dy, given that y = 1 when x = 1.