Question

Please solve this question - Integration Chapter

Answer 1

$\huge \sf {\orange {\underline {\pink{\underline {❥︎A᭄ɴsᴡᴇʀ࿐ :−}}}}}$

Given:

$\displaystyle\int\,\frac{(a^x+b^x)^2}{a^xb^x}$

$=\displaystyle\int\,\frac{(a^{2x}+b^{2x}+2\,a^xb^x)}{a^xb^x}\;dx=∫$

$=\displaystyle\int\,[\frac{ a^{2x}}{ a^xb^x}+\frac{b^{2x}}{ a^xb^x}+\frac{2 a^xb^x}{a^xb^x}]\;dx=∫[$

$=\displaystyle\int\,[\frac{a^x}{b^x}+\frac{b^x}{a^x}$

$=\displaystyle\int\,[(\frac{a}{b})^x+(\frac{b}{a}$

$=\displaystyle\int\,(\frac{a}{b})^x\,dx+\int\,(\frac{b}{a})^x\,dx+2\int\,dx=∫($

$\sf{We \: know \: that,}\boxed{\bf\int\,a^x\,dx=\frac{a^x}{loga}+c}$

$=\displaystyle\,\frac{(\frac{a}{b})^x}{log\frac{a}{b}}+\frac{(\frac{b}{a})^x}{log\frac{b}{a}}$

$\therefore\bf\,\displaystyle\int\,\frac{(a^x+b^x)^2}{a^xb^x}\;dx=\frac{(\frac{a}{b})^x}{log(\frac{a}{b})}+\frac{(\frac{b}{a})^x}{log(\frac{b}{a})}∴∫$

Answer 2

Step-by-step explanation:

when a carpet is beaten with a stick and Comes out of it. Explain