Antiderivative

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. $\int -2\cos tdt$ is equals to

1. $\sin t+C$
2. $–\sin t+C$
3. $-2\sin t+C$
4. $2\sin t+C$

Q. Evaluate: $\int \frac{1}{\sqrt{1+x}+\sqrt{x}}dx$

1. $\frac{2}{3}(1+x{)}^{\frac{3}{2}}-\frac{2}{3}(x{)}^{\frac{3}{2}}+C$
2. $\frac{4}{3}(1+x{)}^{\frac{3}{2}}-\frac{2}{3}(x{)}^{\frac{3}{2}}$+C$
3. $\frac{3}{2}(1+x{)}^{\frac{3}{2}}-\frac{2}{3}(x{)}^{\frac{3}{2}}$ $+C$
4. $\frac{4}{3}(1+x{)}^{\frac{3}{2}}-\frac{4}{3}(x{)}^{\frac{3}{2}}$ +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. $\int (\frac{1}{x}-x^2-\frac{1}{3})dx$ is equal to

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

Q. Integrate:$\int \frac{dt}{6t-1}$

1. $\frac{1}{6}ln(6t-1)+C$
2. $\frac{1}{12}ln(6t-1)+C$
3. $\frac{1}{6}ln(12t-1)+C$
4. $\frac{6}{1}ln(6t-1)+C$

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

Q.

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

$y=x-\frac{1}{x}+\frac{1}{x^2}$

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

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

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

4. None of these

Q. The antiderivative of cos x is .

1. sinx
2. cosx
3. -sinx
4. tanx

Q. Evaluate $\int \cos (-2x+3)dx$

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

Q. Evaluate $\int \cos (-2x+3)dx$

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

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

$y=e^{2x}+\frac{1}{x^2}$

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

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

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

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

Q.

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

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

1. $\frac{sin(8x+6)}{8}+\frac{cot(7x+5)}{7}+6secxtanx$

2. $sin\left(8x\right)-cot\left(7x\right)+6secx+c$

3. $\frac{sin(8x+6)}{8}-\frac{cot(7x+5)}{7}+6secx+c$

4. $sin(8x+6)-cot(7x+5)6secx+c$

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 $\int x^2{e}^{x}dx$

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

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.

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

$y=x-\frac{1}{x}+\frac{1}{x^2}$

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

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

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

4. None of these

Q. The antiderivative of cos x is .

1. sinx
2. cosx
3. -sinx
4. tanx

Q. What is the antiderivative of $cosx$ ?

1. sin x
2. cos x
3. - sin x
4. tan x

Q. Evaluate $\int (x^3-e^x+\cos x)dx$

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

Q. Integrate:$\int \frac{dt}{6t-1}$

1. $\frac{1}{6}ln(6t-1)+C$
2. $\frac{1}{12}ln(6t-1)+C$
3. $\frac{1}{6}ln(12t-1)+C$
4. $\frac{6}{1}ln(6t-1)+C$

Q. $\int \left(\frac{t\sqrt{t}+\sqrt{t}}{t^2}\right)dt$ is equal to

1. $2(\sqrt{t}-\frac{1}{\sqrt{t}})+c$
2. $2(\sqrt{t}+\frac{1}{\sqrt{t}})+c$
3. $2(\frac{1}{\sqrt{t}}-\sqrt{t})+c$
4. $2(\sqrt{t}+2\sqrt{t})$

Q. $\int \left(\frac{t\sqrt{t}+\sqrt{t}}{t^2}\right)dt$ is equal to

1. $2(\sqrt{t}-\frac{1}{\sqrt{t}})+c$
2. $2(\sqrt{t}+\frac{1}{\sqrt{t}})+c$
3. $2(\frac{1}{\sqrt{t}}-\sqrt{t})+c$
4. $2(\sqrt{t}+2\sqrt{t})$

Q. If $x=(6y+4)(3y^2+4y+3)$, then $\int xdy$ will be

1. $\frac{1}{3y^2+4y+3}+C$
2. $\frac{(3y^2+4y+3{)}^2}{2}+C$
3. $3y^2+4y+3+C$
4. $\frac{(6y+4)}{3y^2+4y+3}+C$

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.

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

$Y=3x^2-\frac{1}{\sqrt{x}}$

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

2. $x^3-2\sqrt{x}$

3. $6x+\frac{1}{2(x{)}^{3/2}}$

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

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