Saved Bookmarks
| 1. |
Integrate the following w.r.t. x. (i) `4x^(3)` , (ii) `x-1/x` , (iii) `1/(2x+3)` , (iv) `cos (4x+3)` (v) `cos^(2) x` |
|
Answer» (i) `int 4x^(3) dx=4(x^(3+1)/(3+1))+c=(4x^(4))/(4)+c=x^(4)+c` (ii) `int(x-1/x)dx=intxdx-int1/xdx=x^(2)/2-ln x+c` (iii) `int(dx)/(2x+3)=(ln(2x+3))/2+c` (iv) `int cos(4x+3)dx=(sin(4x+3))/(4)+c` (v) `intcos^(2) xdx=int(2 cos^(2) x)/(2)dx=int((1+cos 2x))/2dx=1/2intdx+1/2 int cos2xdx` `=x/2+1/2(sin 2x)/2+c=x/2+1/4 sin 2x+c` |
|