समाकलन गणित - समाकलन

• A
  $a=\frac{-1}{10}, b=\frac{-2}{5}$
• B
  $a=\frac{1}{10}, b=-\frac{2}{5}$
• ✓
  $a=\frac{-1}{10}, b=\frac{2}{5}$
• D
  $a=\frac{1}{10}, b=\frac{2}{5}$

Answer: C.

• ✓
  $(x+1) \tan ^{-1} \sqrt{x}-\sqrt{x}+c$
• B
  $x \tan ^{-1} \sqrt{x}-\sqrt{x}+c$
• C
  $\sqrt{x}-x \tan ^{-1} \sqrt{x}+c$
• D
  $\sqrt{x}-(x+1) \tan ^{-1} \sqrt{x}+c$

Answer: A.

• A
  $\log |1+\cos x|+c$
• B
  $\log |x+\sin x|+c$
• C
  $x-\tan \frac{x}{2}+c$
• ✓
  $x \cdot \tan \frac{x}{2}+c$

Answer: D.

• A
  $\frac{1}{5 x}\left(4+\frac{1}{x^2}\right)^{-5}+C$
• B
  $\frac{1}{5}\left(4+\frac{1}{x^2}\right)^{-5}+C$
• C
  $\frac{1}{10 x}(1+4)^{-5}+C$
• ✓
  $\frac{1}{10}\left(\frac{1}{x^2}+4\right)^{-5}+C$

Answer: D.

• A
  $x+\frac{x^2}{2}+\frac{x^3}{3}-\log |1-x|+C$
• B
  $x+\frac{x^2}{2}-\frac{x^3}{3}-\log |1-x|+C$
• C
  $x-\frac{x^2}{2}-\frac{x^3}{3}-\log |1+x|+C$
• ✓
  $x-\frac{x^2}{2}+\frac{x^3}{3}-\log |1+x|+C$

Answer: D.