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100
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60
Questions
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Q1. ∫12x−1dx\int \frac{1}{2x-1} dx∫2x−11dx
12log∣2x−1∣+C\frac{1}{2} \log|2x-1| + C21log∣2x−1∣+C
log∣2x−1∣+C\log|2x-1| + Clog∣2x−1∣+C
−12log∣2x−1∣+C-\frac{1}{2} \log|2x-1| + C−21log∣2x−1∣+C
2log∣2x−1∣+C2 \log|2x-1| + C2log∣2x−1∣+C
Q2. ∫(3sin2x+cos2x)dx\int (3\sin^2 x + \cos^2 x) dx∫(3sin2x+cos2x)dx
2x–12sin2x+C2x – \frac{1}{2}\sin 2x + C2x–21sin2x+C
x+sin2x+Cx + \sin 2x + Cx+sin2x+C
2x+12cos2x+C2x + \frac{1}{2}\cos 2x + C2x+21cos2x+C
x–cos2x+Cx – \cos 2x + Cx–cos2x+C
Q3. ∫e3−2xdx\int e^{3-2x} dx∫e3−2xdx
e3−2x+Ce^{3-2x} + Ce3−2x+C
12e3−2x+C\frac{1}{2} e^{3-2x} + C21e3−2x+C
−12e3−2x+C-\frac{1}{2} e^{3-2x} + C−21e3−2x+C
−13e3−2x+C-\frac{1}{3} e^{3-2x} + C−31e3−2x+C
Q4. ∫sin(ex)exdx\int \sin(e^x) e^x dx∫sin(ex)exdx
cos(ex)+C\cos(e^x) + Ccos(ex)+C
−cos(ex)+C-\cos(e^x) + C−cos(ex)+C
sin(ex)+C\sin(e^x) + Csin(ex)+C
excos(ex)+Ce^x \cos(e^x) + Cexcos(ex)+C
Q5. ∫elogx−2dx\int e^{\log x^{-2}} dx∫elogx−2dx
1x+C\frac{1}{x} + Cx1+C
−1x+C-\frac{1}{x} + C−x1+C
x−3−3+C\frac{x^{-3}}{-3} + C−3x−3+C
x22+C\frac{x^2}{2} + C2x2+C
Q6. ∫(sec2x−csc2x)dx\int (\sec^2 x - \csc^2 x) dx∫(sec2x−csc2x)dx
tanx−cotx+C\tan x - \cot x + Ctanx−cotx+C
tanx+cotx+C\tan x + \cot x + Ctanx+cotx+C
tanx+2cotx+C\tan x + 2\cot x + Ctanx+2cotx+C
2tanx+cotx+C2\tan x + \cot x + C2tanx+cotx+C
Q7. ∫sin2x1+cos2xdx\int \frac{\sin 2x}{1 + \cos 2x} dx∫1+cos2xsin2xdx
−log∣cosx∣+C-\log|\cos x| + C−log∣cosx∣+C
log∣secx∣+C\log|\sec x| + Clog∣secx∣+C
12log∣secx∣+C\frac{1}{2} \log|\sec x| + C21log∣secx∣+C
−12log∣cosx∣+C-\frac{1}{2} \log|\cos x| + C−21log∣cosx∣+C
Q8. ∫cos2x−1cos2x+1dx\int \frac{\cos 2x - 1}{\cos 2x + 1} dx∫cos2x+1cos2x−1dx
tanx−x+C\tan x - x + Ctanx−x+C
x−tanx+Cx - \tan x + Cx−tanx+C
cotx−x+C\cot x - x + Ccotx−x+C
x−cotx+Cx - \cot x + Cx−cotx+C
Q9. ∫cos2xcosxdx\int \frac{\cos 2x}{\cos x} dx∫cosxcos2xdx
2sinx−log∣secx+tanx∣+C2\sin x - \log|\sec x + \tan x| + C2sinx−log∣secx+tanx∣+C
sinx−log∣secx+tanx∣+C\sin x - \log|\sec x + \tan x| + Csinx−log∣secx+tanx∣+C
2sinx+log∣secx+tanx∣+C2\sin x + \log|\sec x + \tan x| + C2sinx+log∣secx+tanx∣+C
2cosx−log∣secx+tanx∣+C2\cos x - \log|\sec x + \tan x| + C2cosx−log∣secx+tanx∣+C
Q10. ∫1(3−x)2dx\int \frac{1}{(3-x)^2} dx∫(3−x)21dx
−13−x+C-\frac{1}{3-x} + C−3−x1+C
13−x+C\frac{1}{3-x} + C3−x1+C
−log∣3−x∣+C-\log|3-x| + C−log∣3−x∣+C
−1(3−x)3+C\frac{-1}{(3-x)^3} + C(3−x)3−1+C
Q11. ∫sin−1(cosx)dx\int \sin^{-1} (\cos x) dx∫sin−1(cosx)dx
πx2+x22+C\frac{\pi x}{2} + \frac{x^2}{2} + C2πx+2x2+C
π2−x+C\frac{\pi}{2} - x + C2π−x+C
πx2−x22+C\frac{\pi x}{2} - \frac{x^2}{2} + C2πx−2x2+C
πx2−x2+C\frac{\pi x}{2} - x^2 + C2πx−x2+C
Q12. ∫ex(x−1x2)dx\int e^x \left(\frac{x-1}{x^2}\right) dx∫ex(x2x−1)dx
exx2+C\frac{e^x}{x^2} + Cx2ex+C
exx+C\frac{e^x}{x} + Cxex+C
exlog∣x∣+Ce^x \log|x| + Cexlog∣x∣+C
−exx+C-\frac{e^x}{x} + C−xex+C
Q13. ∫dx1−4x\int \frac{dx}{\sqrt{1-4^x}}∫1−4xdx
1log2sin−1(2x)+C\frac{1}{\log 2} \sin^{-1}(2^x) + Clog21sin−1(2x)+C
sin−1(2x)+C\sin^{-1}(2^x) + Csin−1(2x)+C
1log4sin−1(2x)+C\frac{1}{\log 4} \sin^{-1}(2^x) + Clog41sin−1(2x)+C
2log2sin−1(2x)+C\frac{2}{\log 2} \sin^{-1}(2^x) + Clog22sin−1(2x)+C
Q14. ∫etan−1x1x+xxdx\int e^{\tan^{-1} \sqrt{x}} \frac{1}{\sqrt{x} + x \sqrt{x}} dx∫etan−1xx+xx1dx
etan−1x+Ce^{\tan^{-1} \sqrt{x}} + Cetan−1x+C
2etan−1x+C2 e^{\tan^{-1} \sqrt{x}} + C2etan−1x+C
12etan−1x+C\frac{1}{2} e^{\tan^{-1} \sqrt{x}} + C21etan−1x+C
etan−1x+Ce^{\tan^{-1} x} + Cetan−1x+C
Q15. ∫ex+exe−1ex+xedx\int \frac{e^{x}+e x^{e-1}}{e^{x}+x^{e}} d x∫ex+xeex+exe−1dx
1elog∣ex+xe∣+C\frac{1}{e} \log|e^x + x^e| + Ce1log∣ex+xe∣+C
log∣ex+xe∣+C\log|e^x + x^e| + Clog∣ex+xe∣+C
elog∣ex+xe∣+Ce \log|e^x + x^e| + Celog∣ex+xe∣+C
log∣ex+xe−1∣+C\log|e^x + x^{e-1}| + Clog∣ex+xe−1∣+C
...and 45 more challenging questions available in the interactive simulator.
