Integrals

Integration by trigonometric substitution — ∫dx/√(a²-x²) types

NCERT Class 12

Evaluate ∫₀^π xsinx dx using integration by parts

Reduction formula for ∫sinⁿ(x) dx — derive and apply for n=6

JEE Advanced 2022

Evaluate ∫sin²x dx using double angle formula

Partial fractions — decompose and integrate (2x+1)/((x+1)(x²+1))

CBSE 2024

Evaluate ∫(0 to 1) x^n · ln(x) dx using integration by parts

JEE Advanced 2023

Integration by parts — evaluate ∫x·eˣ dx step by step

NCERT Class 12

Solve ∫dx/√(1-x²) — inverse trigonometric integral

NCERT Class 12

Evaluate ∫dx/(x² + 4x + 13) using completing the square

JEE Main 2021

Evaluate ∫(0 to π/2) log(sin x) dx — JEE Advanced level definite integral

JEE Advanced 2019

Integration Using Trigonometric Substitution — ∫dx/√(a²-x²)

NCERT Class 12

∫₀^π/2 log(sin x) dx — Famous Definite Integral

JEE Advanced 2024

Evaluate ∫eˣ(sin x + cos x) dx — Special eˣ Integral

JEE Main 2024 Shift 2

Integration by Partial Fractions — ∫dx/((x-1)(x+2))

CBSE 2025 Sample Paper

∫dx/(x² + a²) — Standard Integral Form

JEE Main 2023

Evaluate ∫₀¹ √(1-x²) dx — Area Under Semicircle

JEE Advanced 2023

Evaluate ∫sin x dx from 0 to π

CBSE 2024 Board Exam

Integrate ∫x²dx — Basic Power Rule

NCERT Class 12

Integration by Parts — ∫x·eˣ dx

JEE Main 2024