Antiderivative

Q. Find the integral $\int \frac{x+1}{x^2+2x-4}dx$

1. $\ln (x^2+2x-4)+C$
2. $\frac{1}{2}\ln (x^2+2x)+C$
3. $\frac{1}{2}\ln (x^2+2x-4)+C$
4. $\frac{1}{2}\ln (x+1)+C$

Q. $\int 2x(x-x^{-3})dx$ is equal to

1. $\frac{2x^3}{3}+\frac{2}{x}+c$
2. $\frac{2x^3}{3}-\frac{2}{x}+c$
3. $\frac{x^3}{3}-\frac{2}{x}+c$
4. $\frac{x^3}{3}+\frac{2}{x}+c$

Q. Evaluate: $\int (3e^{3x}+e^{-x})dx$

1. $e^{3x}+e^{-x}+C$
2. $e^{3x}-e^{-x}+C$
3. $e^{3x}+e^{-2x}+C$
4. $3e^{3x}+e^{-x}+C$

Q. Evaluate: $\int \left(\cos \right(x)-\frac{3}{x^5})dx$

1. $\sin x+\frac{3}{4x^4}+C$
2. $\sin x-\frac{3}{4x^4}+C$
3. $\sin x+\frac{4}{5x^4}+C$
4. $\sin x+\frac{3}{5x^5}+C$

Q.

Find the integral of the given function w.r.t x

$y=cos(8x+6)+cose{c}^2(7x+5)+6secxtanx$

1. 

2. 

3. 

4. 

Q. Find the integral $\int \frac{2x}{x^2-4}dx$

1. $\ln \left(2x\right)+C$
2. $e^{x^2-4}+C$
3. $\ln (x^2-4)+C$
4. $\frac{e^{x^2-4}}{2x}+C$

Q. Evaluate $\int e^x\sin xdx$

1. $-e^x(\cos x-\sin x)$
2. $\frac{-e^x}{2}(\cos x-\sin x)$
3. $\frac{-e^x}{2}(\cos x+\sin x)$
4. $-e^x(\cos x+\sin x)$

Q.

Find the integral of the given function w.r.t - x

$y=\frac{si{n}^2\sqrt{x}}{2\sqrt{x}}$

1. $\frac{1}{2}{x}^3+\frac{1}{3}sin3x+c$

2. $\frac{1}{2}\sqrt{x}-\frac{1}{4}sin2\sqrt{x}+c$

3. $\frac{1}{2}\sqrt{x}-\frac{1}{4}sin\sqrt{x}+c$

4. None of these

Q. Evaluate $\int {(x+\frac{1}{x})}^{2}dx$

1. $\frac{x^3}{3}-\frac{1}{x}+x+c$
2. $\frac{x^3}{3}+\frac{1}{x}+2x+c$
3. $\frac{x^3}{3}-\frac{1}{x}+2x+c$
4. $\frac{x^3}{3}+\frac{1}{x}+x+c$

Q.

Find the integral of the given function w.r.t x

$y=sin6x+10se{c}^{2}x-cosecxcotx$

1. $6cos6x+20se{c}^{2}xtanx+cosecxcotx+cose{c}^{3}x+c$

2. $cos6x+10tanx+cosecx+c$

3. $-\frac{cos\left(6x\right)}{6}+10tanx-\left(cosecx\right)+c$

4. $-cosec6x+10tanx+cosecx+c$

Q. N(g) + O+(g) ---> N+(g) + O(g) is the above process spon†an eous?

Q. Evaluate $\int x{e}^{x}dx$

1. $e^x(x+1)$
2. $\frac{e^x}{(x-1)}$
3. $e^x(x-1)$
4. $\frac{e^x}{(x+1)}$

Q.

Integrate the following w.r.t $x:\frac{1}{2x+3}$

1. ln |2x + 3| + c

2. $\frac{ln|2x+3|}{2}+c$

3. $\frac{ln(2x+3)}{2x+3}+c$

4. None of these

Q. $\int (\sin x+x^2)dx$ is equal to:

1. $2x+\cos x+C$
2. $\frac{x^2}{3}+\cos x+C$
3. $\frac{x^3}{3}-\cos x+C$
4. $2x-\cos x+C$

Q.

Find the integral of the given function w.r.t x

$y=sin\left(8x\right)+x$

1. $-\frac{cos8x}{8}+\frac{x^2}{2}+c$

2. $\frac{8cos8x}{8}+1+c$

3. $\frac{cos8x}{8}+\frac{x^2}{2}+c$

4. $\frac{cos8x}{8}+1+c$

Q. how will i unders†an d that △ H of a given reaction is +ve or -ve?

Q. Evaluate $\int \frac{3}{-3x+6}dx$

1. $\ln (-3x+6)$
   
2. $-\ln (-3x+6)$
   
3. $\frac{-\ln (-3x+6)}{3}$
   
4. $\frac{\ln (-3x+6)}{3}$

Q. Evaluate:
i. $\int (\sin x+\cos x)dx$
ii. $\int (3x^2+4)dx$

1. $i.-\cos x+\sin x+C$
   $ii.x^3+4x+C$
2. $i.-\cos x-\sin x+C$
   $ii.x^3-2x+C$
3. $i.-\cos x-\sin x+C$
   $ii.x^3+2x+C$
4. $i.\cos x+\sin x+C$
   $ii.x^3-4x+C$

Q. Evaluate $\int \frac{6}{-3x+6}dx$

1. $\frac{e^{-3x+6}}{2}+C$
2. $-2\ln (-3x+6)+C$
3. $-2e^{-3x+6}+C$
4. $\frac{\ln (-3x+6)}{2}+C$

Q. Evaluate $\int x^2\sin xdx$

1. $-x^2\cos x+2(x\sin x+\cos x)$
2. $-x^2\cos x-2(x\sin x+\cos x)$
3. $x^2\cos x+(2x\sin x+\cos x)$
4. $x^2\cos x-(2x\sin x-\cos x)$

Q. Evaluate $\int {\sec }^2(-3x+4)dx$

1. $\frac{-\tan (-3x+4)}{3}+C$
2. $\frac{\tan (-3x+4)}{4}+C$
3. $\frac{\tan (-3x+4)}{3}+C$
4. $\frac{-\cot (-3x+4)}{4}+C$

Q. Evaluate: $\int \left(\cos \right(x)+x^2)dx$

1. $\sin x+\frac{x^3}{2}+C$
2. $\sin x+\frac{x^3}{6}+C$
3. $\sin x+\frac{x^2}{3}+C$
4. $\sin x+\frac{x^3}{3}+C$

Q. Evaluate: $\int {\sin }^{2}xdx$

1. $\frac{x}{2}-\frac{\sin 2x}{4}+C$
2. $\frac{x}{2}-\frac{\sin 2x}{2}+C$
3. $\frac{x}{4}-\frac{\sin 2x}{4}+C$
4. $\frac{x}{2}-\frac{\sin 2x}{3}+C$

Q. $\int (se{c}^{2}x+e^{3x})dx$ is equals to

1. $\sec x+\frac{e^{3x}}{3}+C$
2. $\tan x+\frac{e^{3x}}{3}+C$
3. $\tan x+e^{3x}+C$
4. $\sec x\tan x+e^{3x}+C$

Q. Evaluate the integral ${\int }_0^{\frac{\pi }{2}}\sin xdx$

1. $0$
2. $-1$
3. $1$
4. $2$