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\int \left [ \left ( 3x-2 \right )\left ( x+4 \right ) \right ]^{7\left ( 3x+5 \right )dx}

  • Option 1)

    \frac{\left [ \left ( 3x-2 \right )\left ( x+4 \right ) \right ]^{8}}{8}+C

  • Option 2)

    \frac{\left [ \left ( 3x-2 \right )\left ( x+4 \right ) \right ]^{8}}{12}+C

  • Option 3)

    \frac{\left [ \left ( 3x-2 \right )\left ( x+4 \right ) \right ]^{8}}{16}+C

  • Option 4)

    \frac{\left [ \left ( 3x-2 \right )\left ( x+4 \right ) \right ]^{8}}{24}+C

 

Answers (1)

best_answer

As we learned,

 

Type of integration by substitution -

\int (ax+b)^{n}f(x)dx

or    \int\frac{f(x)}{(ax+b)^{n}}dx

- wherein

Where n is any rational number. (+ive or -ive)

Let (ax+b)=t

\therefore dx=\frac{dt}{a} .

 

 

t=\left ( 3x-2 \right )\left ( x+4 \right )=3x^{2}+10x-8

dt=\left ( 6x+10 \right )dx\Rightarrow \left ( 3x+5 \right )dx=\frac{dt}{2}

\Rightarrow \int \frac{t^{7}dt}{2}=\frac{t^{8}}{16}+C


Option 1)

\frac{\left [ \left ( 3x-2 \right )\left ( x+4 \right ) \right ]^{8}}{8}+C

Option 2)

\frac{\left [ \left ( 3x-2 \right )\left ( x+4 \right ) \right ]^{8}}{12}+C

Option 3)

\frac{\left [ \left ( 3x-2 \right )\left ( x+4 \right ) \right ]^{8}}{16}+C

Option 4)

\frac{\left [ \left ( 3x-2 \right )\left ( x+4 \right ) \right ]^{8}}{24}+C

Posted by

gaurav

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