1.Evaluate $\int \frac{2x+5}{x^2+5x-7} dx$.
2.Evaluate $\int \frac{e^{\tan^{-1}x}}{1+x^2} dx$.
3.Find $\int \frac{\sin(\log x)}{x} dx$.
4.Evaluate $\int \frac{\sec^2(\sqrt{x})}{\sqrt{x}} dx$.
5.Find $\int \frac{1}{x+x\log x} dx$.
6.Evaluate $\int \frac{e^{2x}-1}{e^{2x}+1} dx$. (Hint: Divide numerator and denominator by $e^x$).
7.Find $\int \frac{\cos x}{1+\sin^2 x} dx$.
8.Evaluate $\int \frac{1}{\sqrt{x}(1+\sqrt{x})} dx$.
9.Find $\int \frac{x^2}{1+x^6} dx$.
10.Evaluate $\int \frac{\sin 2x}{a^2\cos^2 x + b^2\sin^2 x} dx$.
11.Find $\int \frac{10x^9 + 10^x \log_e 10}{x^{10} + 10^x} dx$.
12.Evaluate $\int \frac{\sec^2(1+\log x)}{x} dx$.
13.Find $\int \frac{x^3}{\sqrt{1-x^8}} dx$.
14.Evaluate $\int \frac{e^x(1+x)}{\cos^2(x e^x)} dx$.
15.Find $\int \frac{dx}{e^x + e^{-x}}$.
16.Evaluate $\int \sin^3 x \cos^2 x dx$.
17.Find $\int \cos^4 x dx$.
18.Evaluate $\int \frac{\sin x}{\sin(x-a)} dx$.
19.Find $\int \frac{1}{1+\cos x} dx$.
20.Evaluate $\int \sin 4x \sin 8x dx$.
21.Find $\int \sqrt{1+\sin 2x} dx$.
22.Evaluate $\int \frac{\cos 2x}{\cos x + \sin x} dx$.
23.Find $\int \tan^4 x dx$.
24.Evaluate $\int \sec^4 x dx$.
25.Find $\int \frac{dx}{\sin^2 x \cos^2 x}$.
26.Evaluate $\int \frac{\cos 2x}{(\sin x + \cos x)^2} dx$.
27.Find $\int \frac{\sin(x-a)}{\sin(x+a)} dx$.
28.Evaluate $\int \frac{1}{\sin x \cos^3 x} dx$.
29.Find $\int \cos x \cos 2x \cos 3x dx$.
30.Evaluate $\int \frac{\sin x - \cos x}{\sqrt{1+\sin 2x}} dx$.
31.Evaluate $\int \frac{dx}{x^2+4x+13}$.
32.Find $\int \frac{dx}{\sqrt{5-4x-x^2}}$.
33.Evaluate $\int \frac{x+2}{x^2-5x+6} dx$.
34.Find $\int \frac{2x+1}{\sqrt{x^2+4x+5}} dx$.
35.Evaluate $\int \frac{dx}{x(x^4+1)}$. (Hint: Multiply and divide by $x^3$).
36.Find $\int \frac{x^2}{x^2+1} dx$.
37.Evaluate $\int \frac{x}{(x-1)(x^2+1)} dx$ using partial fractions.
38.Find $\int \frac{3x-2}{(x+1)^2(x+3)} dx$.
39.Evaluate $\int \frac{x^2}{(x^2+1)(x^2+4)} dx$.
40.Find $\int \sqrt{x^2+2x+5} dx$.
41.Evaluate $\int \frac{x^2+1}{x^4+1} dx$.
42.Find $\int \frac{dx}{x[(\log x)^2 - 5\log x + 6]}$.
43.Evaluate $\int \frac{dx}{e^{2x}-3e^x+2}$.
44.Find $\int \frac{dx}{(x-1)\sqrt{x+2}}$.
45.Evaluate $\int \frac{\cos x}{(1-\sin x)(2-\sin x)} dx$.
46.Evaluate $\int x \tan^{-1} x dx$.
47.Find $\int x^2 \sin x dx$.
48.Evaluate $\int \sec^3 x dx$.
49.Find $\int e^x \left(\frac{x-1}{x^2}\right) dx$.
50.Evaluate $\int e^{2x} \sin 3x dx$.
51.Find $\int \log(x^2+1) dx$.
52.Evaluate $\int \sin^{-1}\left(\frac{2x}{1+x^2}\right) dx$.
53.Find $\int e^x \frac{x}{(x+1)^2} dx$.
54.Evaluate $\int \cos^{-1}\sqrt{x} dx$.
55.Find $\int \frac{x \sin^{-1} x}{\sqrt{1-x^2}} dx$.
56.Evaluate $\int \left[\log(\log x) + \frac{1}{(\log x)^2}\right] dx$.
57.Find $\int e^x \left(\frac{1+\sin x}{1+\cos x}\right) dx$.
58.Evaluate $\int x^3 e^{x^2} dx$.
59.Find $\int e^x \sec x(1+\tan x) dx$.
60.Evaluate $\int \sin(\log x) dx$.
61.Evaluate $\int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx$.
62.Evaluate $\int_0^1 x(1-x)^n dx$.
63.Find $\int_0^{\pi/2} \log(\tan x) dx$.
64.Evaluate $\int_{-\pi/2}^{\pi/2} \sin^7 x dx$.
65.Find $\int_0^\pi \frac{x \sin x}{1+\cos^2 x} dx$.
66.Evaluate $\int_{-1}^1 |x| dx$.
67.Find $\int_0^2 |x^2+2x-3| dx$.
68.Evaluate $\int_0^{\pi/2} \frac{\sin^n x}{\sin^n x + \cos^n x} dx$.
69.Find $\int_0^{\pi} \log(1+\cos x) dx$.
70.Evaluate $\int_{-\pi/4}^{\pi/4} x^3 \sin^2 x dx$.
71.Find $\int_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a-x}} dx$.
72.Evaluate $\int_0^{1.5} [x] dx$, where $[x]$ denotes the greatest integer function.
73.Find $\int_0^\pi \cos^2 x dx$.
74.Evaluate $\int_{-2}^2 (x^3 \cos x + x + 1) dx$.
75.Find $\int_0^{\pi/2} \sin 2x \log(\tan x) dx$.
