(i) Match the following: ∫sin3xdx, ∫xsinxdx

Question

(i) Match the following :

A	B
\(\int sin\,3xdx\)	\(\frac{x}{2} + \frac{1}{4} sin\,2x + c\)
\(\int x\,sin\,xdx\)	log(\(1+x^2\)) + c
\(\int \frac{2x}{1+x^2}dx\)	-\(\frac{1}{3}\) cos3x + c
\(\int cos^2\, xdx\)	2cosxsinx + c
	-xcosx + sinx + c log|tanx| + c

(ii) Consider the function f(x) = \(\frac{x^4}{x+1}\) Evaluate ∫f(x)dx

Answer 1

A	B
\(\int sin\,3xdx\)	-\(\frac{1}{3}\)cos 3x + c
\(\int x\,sin\,xdx\)	-xcos x + sin x + c
\(\int \frac{2x}{1+x^2}dx\)	log(\(1+x^2\)) + c
\(\int cos^2\, xdx\)	\(\frac{x}{2} + \frac{1}{4} sin\,2x + c\)

(ii) Here the numerator is of degree 4 and denominator of degree 1. So to make it a proper fraction we have to divide Nr by Dr.