Question

1+x+√x+ x/
√x+√1+x

dx =​

Answer 1

${\large{\boxed{\sf{∫(1+x+\sqrt{x}+\frac{x}{\sqrt{x}}+\sqrt{1}+x).dx}}}}$

= ${\large{\boxed{\sf{∫(1+x+\sqrt{x}+\sqrt{x}+1+x).dx}}}}$

= ${\large{\boxed{\sf{∫(2+2x+2\sqrt{x}).dx}}}}$

= ${\large{\boxed{\sf{2∫(1+x+\sqrt{x}).dx}}}}$

= ${\large{\boxed{\sf{2[∫1.dx+∫x.dx+∫{x}^{\frac{1}{2}}.dx]}}}}$

= ${\large{\boxed{\sf{2[x+\frac{x²}{2}+\frac{{x}^{\frac{3}{2}}}{\frac{3}{2}}+c]}}}}$

= ${\large{\boxed{\red{\sf{\frac{6x+3x²+4\sqrt{x³}}{3}+c}}}}}$

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