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### Anti Derivative

23. ${\int }_{0}^{1}\frac{2x}{1+{x}^{2}}dx$ [2075]

0

log2

2

1

24. $\int \frac{dx}{x\left(1+lnx{\right)}^{2}}=$ [2075]

$-\frac{1}{1+lnx}+c$

$\frac{1}{1+lnx}+c$

$\frac{1}{lnx}+c$

$\frac{1}{x\left(1+lnx\right)}+c$

24. $\int \frac{dx}{si{n}^{2}x}=$ [2074]

a + x + c

-a + x + c

tanx + c

tanx + c

25. ${\int }_{0}^{1}\frac{dx}{1+{x}^{2}}=$ [2074]

π / 4

π / 2

0

tanx + c

22. $\int \frac{dx}{1-{x}^{2}}=$ [2073]

cos-1x + c

$\frac{1}{2}ln|\frac{1-x}{1+x}|+c$

sin-1x + c

$\frac{1}{2}ln|\frac{1+x}{1-x}|$

23. ${\int }_{1}^{2}\frac{sin\left(lnt\right)}{1}dt=$= [2073]

1-cos(ln2)

cos2

cos(ln2)

1+cos(ln2)

25. The area bounded by the a-axis and the curve y = x3 and ordinates of x - 2 and x - 4 is [2073]

60 sq units

256 sq units

240 sq units

272 sq. units

23. ${\int }_{0}^{1}\frac{2xdx}{\sqrt{1-{x}^{2}}}$ [2072]

1/2

1

0

2

24. $\int xsinxdx=$ [2072]

Sinx - xCosx + C

Sinx + xCosx + C

Cosx + xSinx + C

-Sinx + xCosx + C

25. Area bounded by the x-axis and the curve y = 3x2 and the ordinate of x = 2 and x = 4 is [2072]

27

8

19

0

24. $\int \frac{dx}{1-cosx}$ = [2071]

tan x/2

-cot x/2

cos x/2

-tan x/2

25. ${\int }_{0}^{\frac{1}{2}}\frac{cosx}{1+sinx}dx$ [2071]

ln|2|

0

1

25. Which one of the following is the area enclosed by curve y = 3x, the x-axis and the ordinate x = 0, x = 4? [2070]

12

16

20

24

9. The integral $\int \frac{dx}{\left({e}^{x}-{e}^{-x}{\right)}^{2}}$ is equal to [2070]

$\frac{-1}{2|{e}^{2}+1|}+c$

$\frac{-1}{|{e}^{2x}+1|}+c$

$\frac{-1}{2|{e}^{x}+{e}^{-x}|}+c$

$\frac{-1}{2|{e}^{2x}+1|}+c$

I there is