Sin3x formula

Tip: See my list of the Most Common Mistakes in English. It will teach you how to avoid mis­takes with com­mas, pre­pos­i­tions, ir­reg­u­lar verbs, and much more. Integrating the third power of $\sin(x)$ (or any odd power, for that matter), is an easy task (unlike The same approach works for any odd power of $\sin(x)$ (or $\cos(x)$), only the resulting expressions get slightly more complicated. For example, $$ ∫ \sin^5(x)\,dx = ∫ \sin(x)(\sin^2(x))^2\,dx = ∫ \sin(x)(1-\cos^2(x))^2\,dx \\ = ∫ -(1-u^2)^2\,du = ∫ (-u^4+2u^2-1)\,du = -\frac3 - u + c \\ = -\frac15 \cos^5(x) + \frac23 \cos^3(x)-\cos(x) + c\,. $$

Tip: See my list of the Most Common Mistakes in English. It will teach you how to avoid mis­takes with com­mas, pre­pos­i­tions, ir­reg­u­lar verbs, and much more. Integrating the third power of $\sin(x)$ (or any odd power, for that matter), is an easy task (unlike The same approach works for any odd power of $\sin(x)$ (or $\cos(x)$), only the resulting expressions get slightly more complicated. For example, $$ ∫ \sin^5(x)\,dx = ∫ \sin(x)(\sin^2(x))^2\,dx = ∫ \sin(x)(1-\cos^2(x))^2\,dx \\ = ∫ -(1-u^2)^2\,du = ∫ (-u^4+2u^2-1)\,du = -\frac3 - u + c \\ = -\frac15 \cos^5(x) + \frac23 \cos^3(x)-\cos(x) + c\,. $$