What is `int (1 + cos x)^2 dx`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The integral `int (1 + cos x)^2 dx` has to be determined.

`int (1 + cos x)^2 dx`

=> `int 1 + cos^2 x + 2*cos x dx`

=> `int 1 + (2*cos^2x - 1)/2 + 1/2 + 2*cos x dx`

=> ` int 1 + (1/2)*cos 2x + 1/2 + 2*cos x dx`

=> `int 3/2 + (1/2)*cos 2x + 2*cos x dx`

=> `3x/2 + (1/4)*sin 2x + 2*sin x + C`

The integral `int (1 + cos x)^2 dx = 3x/2 + (1/4)*sin 2x + 2*sin x + C`

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