MCQ 11 Mark$\int(1-x)^{-2} d x=$A$(1+x)^{-1}+c$✓$(1-x)^{-1}+c$C$(1-x)^{-1}-1+c$D$(1-x)^{-1}+1+c$AnswerCorrect option: B. $(1-x)^{-1}+c$(b) $(1-x)^{-1}+c$View full question & answer→
MCQ 21 Mark$\int\left(\frac{e^{2 x}+e^{-2 x}}{e^x}\right) d x$✓$e^x-\frac{1}{3 e^{3 x}}+c$B$e^x+\frac{1}{3 e^{3 x}}+c$C$e^{-x}+\frac{1}{3 e^{3 x}}+c$D$e^{-x}-\frac{1}{3 e^{3 x}}+c$AnswerCorrect option: A. $e^x-\frac{1}{3 e^{3 x}}+c$(a) $e^x-\frac{1}{3 e^{3 x}}+c$View full question & answer→
MCQ 31 Mark$\int\left(x+\frac{1}{x}\right)^3 d x=$A$\frac{1}{4}\left(x+\frac{1}{x}\right)^4+c$✓$\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x-\frac{1}{2 x^2}+c$C$\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x+\frac{1}{x^2}+c$D$\left(x-x^{-1}\right)^3+c$AnswerCorrect option: B. $\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x-\frac{1}{2 x^2}+c$(b) $\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x-\frac{1}{2 x^2}+c$Hint:$\left(x+\frac{1}{x}\right)^3=x^3+3 x+\frac{3}{x}+\frac{1}{x^3}$View full question & answer→
MCQ 41 Mark$\int \frac{d x}{(x-8)(x+7)}=$A$\frac{1}{15} \log \left|\frac{x+2}{x-1}\right|+c$B$\frac{1}{15} \log \left|\frac{x+8}{x+7}\right|+c$✓$\frac{1}{15} \log \left|\frac{x-8}{x+7}\right|+c$D$(x-8)(x-7)+c$AnswerCorrect option: C. $\frac{1}{15} \log \left|\frac{x-8}{x+7}\right|+c$(C) $\frac{1}{15} \log \left|\frac{x-8}{x+7}\right|+c$View full question & answer→
MCQ 51 Mark$\int \frac{d x}{\left(x-x^2\right)}=$✓$\log x-\log (1-x)+c$B$\log \left(1-x^2\right)+c$C$-\log x+\log (1-x)+c$D$\log \left(x-x^2\right)+c$AnswerCorrect option: A. $\log x-\log (1-x)+c$(a) $\log x-\log (1-x)+c$View full question & answer→
MCQ 61 Mark$\int \frac{x+2}{2 x^2+6 x+5} d x=p \int \frac{4 x+6}{2 x^2+6 x+5} d x+\frac{1}{2} \int \frac{d x}{2 x^2+6 x+5}$, then $p =$A$\frac{1}{3}$B$\frac{1}{2}$✓$\frac{1}{4}$D$2$AnswerCorrect option: C. $\frac{1}{4}$(C) $\frac{1}{4}$Hint:$\int \frac{x+2}{2 x^2+6 x+5} d x=\int \frac{\frac{1}{4}(4 x+6)+\frac{1}{2}}{2 x^2+6 x+5} d x$View full question & answer→
MCQ 71 Mark$\int x^2(3)^{x^3} d x=$A$(3)^{x^3}+c$✓$\frac{(3)^{x^3}}{3 \cdot \log 3}+c$C$\log 3(3)^{x^3}+c$D$x^2(3)^{x 3}$AnswerCorrect option: B. $\frac{(3)^{x^3}}{3 \cdot \log 3}+c$(b) $\frac{(3)^{x^3}}{3 \cdot \log 3}+c$Hint:Put $x^3=t$View full question & answer→
MCQ 81 Mark$\int \sqrt{1+x^2} d x=$✓$\frac{x}{2} \sqrt{1+x^2}+\frac{1}{2} \log \left(x+\sqrt{1+x^2}\right)+c$B$\frac{2}{3}\left(1+x^2\right)^{3 / 2}+c$C$\frac{1}{3}\left(1+x^2\right)+c$D$\frac{(x)}{\sqrt{1+x^2}}+c$AnswerCorrect option: A. $\frac{x}{2} \sqrt{1+x^2}+\frac{1}{2} \log \left(x+\sqrt{1+x^2}\right)+c$(a) $\frac{x}{2} \sqrt{1+x^2}+\frac{1}{2} \log \left(x+\sqrt{1+x^2}\right)+c$View full question & answer→
MCQ 91 Mark$\int \frac{\left(x^3+3 x^2+3 x+1\right)}{(x+1)^5} d x=$✓$\frac{-1}{x+1}+c$B$\left(\frac{-1}{x+1}\right)^5+c$C$\log (x+1)+c$D$\log |x+1|^5+c$AnswerCorrect option: A. $\frac{-1}{x+1}+c$(a) $\frac{-1}{x+1}+c$Hint:$x^3+3 x^2+3 x+1=(x+1)^3$View full question & answer→
MCQ 101 MarkThe value of $\int \frac{d x}{\sqrt{1-x}}$ isA$20 \sqrt{1-x}+ C$✓$-2 \sqrt{1-x}+c$C$\sqrt{x}+ C$D$x + C$AnswerCorrect option: B. $-2 \sqrt{1-x}+c$(b) $-2 \sqrt{1-x}+ c$View full question & answer→