[" 3.If "int((x sim x

int(x)/(x+a)dx

int(x)/(x+a)dx

int(x)/(a+x)dx

Read the following text and answer the followig questions on the basis of the same : inte^(x)[f(x) + f'(x)]dx = int e^(x)f(x)dx + int e^(x) f'(x)dx = f(x)e^(x) - int f'(x)e^(x)dx + int f'(x)e^(x)dx = e^(x)f(x) + c int e^(x)(sin x + cos x)dx =

If int g(x)dx = g(x) , then int g(x){f(x) - f'(x)}dx is equal to

Evaluate the followig integrals (i) int xe^x dx " " (ii) int x cos x dx " " (iii) int log x dx " " (iv) int sin^(-1)x dx .

Evaluate the following integrals: (a) int x^8 dx (b) int_2^5 x^2 dx (c ) int (x+sin x) dx

If int_0^(a) f(x) dx = int_0^(a) f(a-x) dx , then the value of int_0^(pi) x. f(sin x) dx =

int x/(a+x) dx

If y=(sin x)^(sin x)sim((sin x)dot oo)), prove that (dy)/(dx)=(y^(2)cot x)/((1-y log sin x))