Indefinite Integration Questions with Solutions

12 questions2 easy9 medium1 hard

Indefinite integration is the reverse of differentiation: it finds a function whose derivative is the given function, plus an arbitrary constant C. This topic covers standard integrals, integration by substitution, integration by parts, integration using partial fractions, and integrals of special forms such as 1/(x^2 + a^2) and 1/sqrt(a^2 - x^2). Choosing the right method is the main skill. Look for a function whose derivative also appears in the integrand (substitution), a product of two different types of functions (integration by parts, choosing u with the ILATE rule), or a rational function that can be split (partial fractions). In multiple-choice questions, differentiating the answer options to check which one gives the integrand can save time. Practise the indefinite integration questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
$\int \frac{x ^{3}}{1 + x ^{4}} d x$ equals
A. $l o g (x^{4} + 1) + C$ B. $\frac{1}{4} l o g (x^{4} + 1) + C$ C. $\frac{1}{2} l o g (x^{4} + 1) + C$ D. None of these
easyAsked in AMU MCA 2016View solution ›
Q2.
$\int x e^{x} d x = ?$
A. $e^{x} (x - 1) + C$ B. $e^{x} (x + 1) + C$ C. $\frac{x ^{2} e ^{x}}{2} + C$ D. $x e^{x} - 1 + C$
easyView solution ›