Integral of the form `int[xf\'(x)+f(x)]dx` can be evaluated by using integration by parts in first integral and leaving second integral as it is.Now answer the question:`int[x^(x+1)(logx+1)+x^x]dx=` (A) `x^(x+2)+c` (B) `x^(x+1)+c` (C) `x^x+x+c` (D) none of these

Integral of the form int[xf\'(x)+f(x)]dx can be evaluated by using integration by parts in first integral and leaving second integral as it is.Now answer the question: int[1/(x^4+1)-(4x^4)/(x^4+1)^2]dx= (A) x^2/(x^4+1)+c (B) x^3/(x^4+1)+c (C) x/(x^4+1)+c (D) none of these

Integral of the form int[xf\'(x)+f(x)]dx can be evaluated by using integration by parts in first integral and leaving second integral as it is.Now answer the question: int(x+sinx)/(1+cosx)dx= (A) xtanx/2+c (B) x/2tanx/2+c (C) x/2tanx+c (D) none of these

Evaluate the following integration int 2^(x)*e^(x)*dx

By using the properties of definite integrals, evaluate the integrals int_0^1x(1-x)^n dx

Integrate : int(dx)/((x+1)^(2)+1)

Integrate I = int(6x^5)/(1+x^6)dx

Find the integral int(a x^2+b x+c)dx

Integrate int(x*e^(x))/((1+x)^(2))dx .

Integrate : int xsqrt(x+x^2)dx

The integral inte^x(f(x)+f\'(x))dx can be solved by using integration by parts such that: I=inte^xf(x)dx+inte^xf\'(x)dx=e^xf(x)-inte^xf\'(x)dx+inte^xf\'(x)dx=e^xf(x)+C , and inte^(ax)(f(x)+(f\'(x))/a)dx=e^(ax)f(x)/a+C ,Now answer the question: inte^x x^x(2+logx)= (A) e^x x^xlogx+C (B) e^x+x^x+C (C) e^x x(logx)^2+C (D) e^x.x^x+C