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  • Can someone help me with this, - Integral Calculus - JEE Main-2

\int \left ( 7x+8 \right )^{10}dx

  • Option 1)

    \frac{\left ( 7x+8 \right )^{11}}{7}+C

  • Option 2)

    \frac{\left ( 7x+8 \right )^{11}}{8}+C

  • Option 3)

    \frac{\left ( 7x+8 \right )^{11}}{77}+C

  • Option 4)

    \frac{\left ( 7x+8 \right )^{11}}{11}+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} .

 

 

7x+8=t

7dx=dt\Rightarrow dx=\frac{dt}{7}

\int \frac{t^{10}dt}{7}=\frac{t^{11}}{77}+C


Option 1)

\frac{\left ( 7x+8 \right )^{11}}{7}+C

Option 2)

\frac{\left ( 7x+8 \right )^{11}}{8}+C

Option 3)

\frac{\left ( 7x+8 \right )^{11}}{77}+C

Option 4)

\frac{\left ( 7x+8 \right )^{11}}{11}+C

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Plabita

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