FAD1014: MATHEMATICS II — Tutorial 1

Centre for Foundation Studies in Science, University of Malaya
Session 2025/2026

Question 1: Indefinite Integrals

Find the indefinite integrals for the following functions.

(a) $\int(3e^{4x} - 5e^{-6x})dx$

(b) $\int (6x^6 + 4x^3 + 8) dx$

(c) $\int(e^y + \sin y) dy$

(d) $\int 4a^{2e^x} dx$

(e) $\int(2 \tan x + 3 \sec x) dx$

(f) $\int \frac{3x^3 - 5x}{x^7} dx$

(g) $\int (4 + 2^x) dx$

(h) $\int 4e^4 dx$

(i) $\int (x + \sec x \tan x) dx$

(j) $\int \frac{\sin^2 x + \cos^2 x}{3^x} dx$

(k) $\int \frac{(xe^{-2x} - 3x)e^x}{2^x} dx$

(l) $\int 5^{7x} dx$

Use appropriate substitution to find:

(a) $\int 3x(x^2 - 2)^3 dx$

(b) $\int \cos^3 x \sin^2 x dx$

(c) $\int x\sqrt{x^2 + 1} dx$

(d) $\int \left(1 + \frac{1}{\mu}\right)^2 \mu^7 d\mu$

(e) $\int \frac{\sec^2 x}{(1 + \tan x)^3} dx$

(f) $\int x^2 \tan(x^3) \sec(x^3) dx$

(g) $\int \frac{t^2 + 2t}{t + 3t + 10} dt$

(h) $\int \frac{\cos(4\theta) - \cos^3(4\theta)}{\sin^3(4\theta)} d\theta$

(i) $\int \frac{(\ln x)^5}{x} dx$

(j) $\int \frac{x^3 + 2x^2 + 5x + 6}{x+2} dx$

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