₀^ x x x ³ x+ x d x=

Step-by-step solution

Let I = ₀^ x x x ³ x+ x d x = ₀^ x x ² x+1 d x = ₀^ ( -x) x ² x+1 d x= ₀^ x ² x+1 d x- ₀^ x x ² x+1 d x = ₀^ x ² x+1 d x-I2 I= ₀^ x ² x+1 d x Put x=t= d x=-d t When x=0, t=1 and when x= , t=-12 I=- ₁⁻¹ d t 1+t² = _ -1 ¹ d t 1+t² =2 ₀¹ d t 1+t² 2 I=2 [ ⁻¹ t ]₀¹=2 ( 4 )= ( ² 2 ) ² 4