Question

hint please, integral 8sin^4(x)

Answer 1

look in the back of the book for "power reduction" formula for sine

Answer 2

pretty good example worked out here
http://www.youtube.com/watch?v=4bP1FuASneY
these are all decent simple videos

Answer 3

\[8sin^{3}(x) sin(x) dx\]
\[sin^{3}(x)=\sqrt{1-cos^{2}(x)}(1-cos^{2}(x))\]
\[put\] \[u=cos(x)\]
\[du=-sin(x)dx\]
so
\[-8 \sqrt{1-u^{2}}(1-u^{2})du\]

Answer 4

matter of fact this particular video is identical to your problem, except it doesn't have the 8, (which changes nothing) and has 4x instead of x, which makes yours easier

Answer 5

myininaya enjoys these i think ... lets see

Answer 6

\[8(\sin^2(x))^2=8(\frac{1}{2}(1-\cos(2x)))^2\]

Answer 7

\[8 \cdot (\frac{1}{2})^2\int\limits_{}^{}(1-2\cos(2x)+\cos^2(2x)) dx\]

Answer 8

still going to be faced with
\[\cos^2(2x)\] so more work to be done

Answer 9

\[2(x-2 \frac{1}{2} \sin(2x)+\int\limits_{}^{}\frac{1}{2}(1+\cos(4x)) dx)\]

Answer 10

\[2x-2\sin(2x)+\int\limits_{}^{}(1+\cos(4x)) dx\]

Answer 11

\[2x-2\sin(2x)+x+\frac{1}{4}\sin(4x)+C\]

Answer 12

I think one of the easiest way
use by parts
\[-\int sin^{3}x cos(x) dx+3/4 \int sin^{2}(2x)dx\]

Answer 13

\[\int sin^{2}(2x) dx=x/2-sin(4x)/8\]
\[\int sin^{3}x cosxdx=sin^{4}(x)/4\]