`inte^xsine^x dx`

(i) int x sin^-1 x dx (ii) int x cos^-1 x dx (iii) int x tan^-1 x dx (iv) int x cot^-1 x dx

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

(i) int sin^-1 x dx (ii) int cos^-1 x dx (iii) int cot^-1 x dx

If u and v are two functions of x then prove that : int uv dx = u int v dx - int [ (du)/(dx) int v dx ] dx Hence, evaluate int x e^(x) dx

Evaluate (i) int(xe^(x))/((x+1)^(2))dx (ii) int x^3e^(-x) dx

int x. a^(x) dx

int x. a^(x) dx

Evaluate the following integrals: (i) int 2x sqrt(1 + x^2)dx " " (ii) int e^(-x^2) x dx " " (iii) int (sin x)/(1 + cos x) dx (iv) int 1/(1 + x^2)dx " " (v) int x (a - x)^8 dx .

Evaluate: (i) int4x^5\ dx (ii) int2sinx\ dx (iii) int3^(x+2)\ dx (iv) int1/2s e c^2x\ dx