prove the following `int e^(g(x)){f(x)*g'(x)+f'(x)}dx=e^(g(x))f(x)+c`

Evaluate the following int[f(x)g''(x)-f''(x)g(x)]dx

int{f(x)g'(x)-f'g(x)}dx equals

int [f(x)g"(x) - f"(x)g(x)]dx is

int{f(x)+-g(x)}dx=int f(x)dx+-int g(x)dx

Which of the follo wing is/are true? f(x)=e^(x) and g(x)=In x, then f(g(x))=x (wherever f(g(x)) is defined )

Let f,g, h be 3 functions such that f(x)gt0 and g(x)gt0, AA x in R where int f(x)*g(x)dx=(x^(4))/(4)+C and int(f(x))/(g(x))dx=int(g(x))/(h(x))dx=ln|x|+C . On the basis of above information answer the following questions: int f(x)*g(x)*h(x)dx is equal to

If the integral I=inte^(sinx)(cosx.x^(2)+2x)dx=e^(f(x))g(x)+C (where, C is the constant of integration), then the number of solution(s) of f(x)=g(x) is/are

Evaluate: if int g(x)dx=g(x), then int g(x){f(x)+f'(x)}dx

int(f(x)g'(x)-f'(x)g(x))/(f(x)g(x)) [ log (g(x))-log(f(x))]dx=