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CBSE Class 12-science Answered

Integration e3x sin 4x dx explain in great detail
Asked by haroonrashidgkp | 23 Oct, 2018, 02:16: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral straight e to the power of 3 straight x end exponent sin 4 xdx straight I equals integral open parentheses sin 4 straight x close parentheses straight e to the power of 3 straight x end exponent dx straight I equals sin 4 straight x integral straight e to the power of 3 straight x end exponent dx minus integral open parentheses straight d over dx sin 4 straight x integral straight e to the power of 3 straight x end exponent dx close parentheses dx straight I equals straight e to the power of 3 straight x end exponent over 3 sin 4 straight x minus integral 4 cos 4 straight x straight e to the power of 3 straight x end exponent over 3 dx straight I equals straight e to the power of 3 straight x end exponent over 3 sin 4 straight x minus 4 over 3 integral cos 4 xe to the power of 3 straight x end exponent dx straight I equals straight e to the power of 3 straight x end exponent over 3 sin 4 straight x minus 4 over 3 open square brackets cos 4 straight x integral straight e to the power of 3 straight x end exponent dx minus integral open parentheses straight d over dx cos 4 straight x integral straight e to the power of 3 straight x end exponent dx close parentheses dx close square brackets straight I equals straight e to the power of 3 straight x end exponent over 3 sin 4 straight x minus 4 over 3 open square brackets straight e to the power of 3 straight x end exponent over 3 cos 4 straight x minus integral open parentheses negative 4 sin 4 straight x cross times straight e to the power of 3 straight x end exponent over 3 close parentheses dx close square brackets straight I equals straight e to the power of 3 straight x end exponent over 3 sin 4 straight x minus 4 over 3 open square brackets straight e to the power of 3 straight x end exponent over 3 cos 4 straight x plus 4 over 3 integral open parentheses sin 4 straight x cross times straight e to the power of 3 straight x end exponent close parentheses dx close square brackets straight I equals straight e to the power of 3 straight x end exponent over 3 sin 4 straight x minus 4 over 3 cross times straight e to the power of 3 straight x end exponent over 3 cos 4 straight x minus 16 over 9 straight I straight I plus 16 over 9 straight I equals straight e to the power of 3 straight x end exponent over 3 sin 4 straight x minus 4 over 9 cross times straight e to the power of 3 straight x end exponent cos 4 straight x 25 over 9 straight I equals straight e to the power of 3 straight x end exponent over 3 sin 4 straight x minus 4 over 9 cross times straight e to the power of 3 straight x end exponent cos 4 straight x straight I equals 9 over 25 open parentheses straight e to the power of 3 straight x end exponent over 3 sin 4 straight x minus 4 over 9 cross times straight e to the power of 3 straight x end exponent cos 4 straight x close parentheses end style
Answered by Sneha shidid | 24 Oct, 2018, 09:27: AM

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