`int_0^picos^3x dx=`

Evaluate each of the following integral: int_0^picos^5x\ dx

Evaluate the following integral: int_0^pixsin^3x\ dx

int_0^(pi) sin3x dx=2/3

int_0^2(x^3+2x)dx=?

Evaluate the following integral: int_0^picos2xlogsinx\ dx

(i) int_0^(pi//2) (sin^3x)/(sin^3x+cos^3x) dx (ii) int_0^(pi//2) (cos^3x)/(sin^3x+cos^3x) dx (iii) int_0^(pi//2) (sin^4x)/(sin^4x+cos^4x) dx (iv) int_0^(pi//2) (cos^5x)/(sin^5x+cos^5x) dx (v) int_0^(pi//2) (sin^5x)/(sin^5x+cos^5x) dx

IF int_0^a sqrtx dx=2a int_0^(pi//2) sin^3 x dx, find int_a^(a+1) x dx .