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Find the integral of \int 4x \sin \left ( x^{2}-1 \right )dx

Option: 1

cos\ \left ( x^{2}+1 \right )+C


Option: 2

cos\ \left ( x^{2}-1 \right )+C


Option: 3

-cos\ \left ( x^{2}+1 \right )+C


Option: 4

-2cos\ \left ( x^{2}-1 \right )+C


Answers (1)

best_answer

Given integral,
\int 4x\ sin\left ( x^{2}-1 \right )dx
Assuming,
x^{2}-1=t
2x\cdot dx=dt
Substituting the values to get,

\int 4x\ sin\left ( x^{2}-1 \right )dx=2\int sin\left ( t \right )dt
\int 4x\ sin\left ( x^{2}-1 \right )dx=-2cos\ t+C
\int 4x\ sin\left ( x^{2}-1 \right )dx=-2cos\ \left ( x^{2}-1 \right )+C

 

Posted by

vinayak

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