List of top Higher Mathematics Questions on Integration

Match the pairs correctly: 

(i)  \( \int \tan x \, dx \)  \(\hspace{3.5cm}\)  \( \log |\sin x| + c \) 
(ii)  \( \int \cot x \, dx \)  \(\hspace{3.5cm}\)  \( \log |\csc x| - \cot x + c \) 
(iii)  \( \int \sec x \, dx \)  \(\hspace{3.5cm}\)  \( \log |\sec x + \tan x| + c \) 
(iv)  \( \int \csc x \, dx \)  \(\hspace{3.5cm}\)  \( -\log |\csc x + \cot x| + c \) 
(v)  \( \int \frac{\cos x}{\sin x} \, dx \)  \(\hspace{3.5cm}\)  \( \log |\sin x| + c \) 
(vi)  Derivative of \( \sin 2x \) with respect to \( x \)  \(\hspace{0.75cm}\)  \( 2 \cos 2x \) 

Evaluate the integral: \[ \int_0^{\pi} \frac{x \sin x}{1 + \cos^2 x} \, dx \]
Evaluate the integral: \[ \int_0^{\pi/2} \frac{\cos^5 x}{\sin^5 x + \cos^5 x} \, dx \]
Evaluate \[ \int_{-1}^{1} \sin^5x \cos^4x \, dx \]
Evaluate \[ \int_{-1}^{2} \left( x^3 - |x| \right) dx. \]
\( \int e^x [f(x) + f'(x)] dx \)= \(\underline{\hspace{2cm}}\)
\( \int \left( \sin^{-1} x + \cos^{-1} x \right) dx\) = \(\underline{\hspace{2cm}}\)