Basic Integration Review

a) \( \displaystyle \int x^3 \, dx \)
b) \( \displaystyle \int e^x \, dx \)
c) \( \displaystyle \int \frac{1}{x} \, dx \)
d) \( \displaystyle \int \sqrt{x} \, dx \)
e) \( \displaystyle \int \sqrt[3]{x^2} \, dx \)
f) \( \displaystyle \int dx \)
g) \( \displaystyle \int 0 \, dx \)
h) \( \displaystyle \int 2 \, dx \)
i) \( \displaystyle \int \pi^2 \, dx \)
j) \( \displaystyle \int e^3 \, dx \)
k) \( \displaystyle \int x^{99} \, dx \)
l) \( \displaystyle \int \frac{1}{x^4} \, dx \)
m) \( \displaystyle \int 3^x \, dx \)
n) \( \displaystyle \int 5 \cdot 2^x \, dx \)

a) \( \displaystyle \int (1 + 2x + e^x) \, dx \)
b) \( \displaystyle \int \frac{x-1}{\sqrt{x}} \, dx \)
c) \( \displaystyle \int (x^7 - 5x^2 + 2x - 3) \, dx \)
d) \( \displaystyle \int \frac{1 + x + x^2}{x} \, dx \)

(a) \( \displaystyle \int_{\pi/4}^{\pi} \sin \theta \, d\theta \)
(b) \( \displaystyle \int_0^{\pi/4} 8 \sec^2 \theta \, d\theta \)
(c) \( \displaystyle \int_{\pi/6}^{\pi/3} 8 \csc t \cot t \, dt \)

(a) \( \displaystyle \int_0^2 (3x^2 - 1) \, dx \)
(b) \( \displaystyle \int_{-1}^0 (2x - e^x + 1) \, dx \)
(c) \( \displaystyle \int_0^{\pi/4} \frac{1 + \cos^2 \theta}{\cos^2 \theta} \, d\theta \)

(a) \( \displaystyle \int_0^1 \frac{2}{1 + t^2} \, dt \)
(b) \( \displaystyle \int_0^9 \sqrt{2x} \, dx \)

(a) \( \displaystyle \int_1^{64} \frac{1 + \sqrt[3]{x}}{\sqrt{x}} \, dx \)
(b) \( \displaystyle \int_1^9 \frac{x - 1}{\sqrt{x}} \, dx \)

(a) \( \displaystyle \int_1^{e^2} \frac{5}{x} \, dx \)
(b) \( \displaystyle \int_0^{\ln 5} (e^x - 1) \, dx \)

(a) \( \displaystyle \int_{-3}^1 e^{v+5} \, dv \)
(b) \( \displaystyle \int_0^2 (6x - 3)(8x^2 + 3) \, dx \)

(a) \( \displaystyle \int_0^{\pi/6} \frac{\sqrt{3} \sin \theta + \sqrt{3} \sin \theta \tan^2 \theta}{\sec^2 \theta} \, d\theta \)
(b) \( \displaystyle \int_0^{\pi/4} \frac{5 - 5 \sin^2 \theta}{\cos^4 \theta} \, d\theta \)