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30 votes
30 votes
Calculus - need work shown

Calculus - need work shown-example-1
User Amen Aziz
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2 Answers

17 votes
17 votes


( - 1)/(2) [\cos(8x(x + 3))]+ c

Calculus - need work shown-example-1
User Misterbee
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2.7k points
25 votes
25 votes

Answer:


\large \text{$ -(1)/(2)\cos (8x^2+24x) + C $}

Explanation:


\large \displaystyle\begin{aligned}\textsf{let }\:u & =8x^2+24x\\\\\implies (du)/(dx) & =16x+24\\ & =2(8x+12)\\\\\implies dx & =(1)/(2(8x+12))\: du\\\end{aligned}


\large\displaystyle\begin{aligned}\int (8x+12) \sin (8x^2+24x)\:dx & = \int (8x+12) \sin (u) \cdot (1)/(2(8x+12))\:du\\\\& = \int ((8x+12)\sin (u))/(2(8x+12))\:du\\\\& = \int (1)/(2)\sin (u)\:du\\\\& = -(1)/(2)\cos (u) + C\\\\& = -(1)/(2)\cos (8x^2+24x) + C\\\\\end{aligned}

User Shreyas
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2.7k points
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