Question

find that value of this ​

Answer 1

solution:-

$\LARGE\rightarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{\int ({x}^{5} + {x}^{7} + {x}^{7} )\: dx}$

$\LARGE\rightarrow \: \: \: \: \: \:\:\mathtt{ \int {x}^{5}dx+ \int {x}^{7}dx + \int {x}^{7} dx}$

$\LARGE\rightarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{\frac{ {x}^{5 + 1} }{5 + 1} + \frac{ {x}^{7 + 1} }{7 + 1} + \frac{ {x}^{9 + 1} }{9 + 1}}$

$\LARGE \rightarrow \: \: \: \: \: \:\:\:\: \: \: \: \: \: \: \: \: \: \ \mathtt{\frac{ {x}^{6} }{6} + \frac{ {x}^{8} }{8} + \frac{ {x}^{10} }{10}}$

$\large \red{\boxed { \mathtt{ANSWER - option \: \: 4th}}}$

NOTE:-

while doing integration the power of variable increases by 1 and resultant is divided by variable.

Additional information

• $\int sin\theta = -cos\theta$
• $\int cos\theta = sin\theta$
• $\int lnx= \frac{1}{x}$
• $\int e^x= e^x$