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Primitive function of a given function

What is the antiderivative of $f\left(x\right)=x\left(\sqrt{x\ }+1\right)$ .

$\frac{2}{5}x^{\frac{5}{2}}+4x^2+c$

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

$\frac{2}{5}x^{\frac{5}{2}}+\frac{1}{2}x^{\frac{1}{2}}+c$

What is the antiderivative of $f\left(x\right)=6x^2$ .

$4x^2+c$

$6x^2+c$

$2x^3+c$

What is the antiderivative of $f\left(x\right)=\frac{\left(x+1\right)}{x^{\frac{1}{2}}}$ .

(2x+3)^3/2+ c

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

(2x+3)^1/2+ c

What is the antiderivative of $f\left(x\right)=\frac{\left(1-x^{\frac{1}{2}}\right)^2}{\sqrt{x}}$ .

$\left(2x+3\right)^{\frac{3}{2}}+c$

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

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

What is the antiderivative of $f\left(x\right)=6x^2$ .

$x^3-x^2+x+c$

$6x^2+2x+c$

$2x^3-x+c$

What is the antiderivative of $f\left(x\right)=\frac{1}{x}$ .

$\ln\left(2x^2\right)+c$

$\ln\left(2x^{ }\right)+c$

$\ln\left(x^{ }\right)+c$

What is the antiderivative of $f\left(x\right)=3x^2-2x+1$ .

$4x^2+c$

$6x^2+c$

$2x^3+c$

What is the antiderivative of $f\left(x\right)=\sqrt{x}+\frac{1}{\sqrt{x}}$ .

$\frac{2}{5}x^{\frac{5}{2}}+4x^2+c$

$\frac{2}{3}x^{\frac{5}{2}}+2x^{\frac{1}{2}}+c$

$\frac{2}{5}x^{\frac{5}{2}}+\frac{1}{2}x^2+c$

What is the antiderivative of $f\left(x\right)=e^x$ .

$\ln\left(e^xx^2\right)+c$

$e^x+c$

$2e^x+c$

What is the antiderivative of $f\left(x\right)=\sqrt{x}$ .

$\frac{2}{5}x^{\frac{5}{2}}+4x^2+c$

$\frac{2}{5}x^{\frac{5}{2}}+c$

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

Questions

Time

Score

Primitive function of a given function

What is the antiderivative of ﻿f(x)=x(x +1)f\left(x\right)=x\left(\sqrt{x\ }+1\right)f(x)=x(x ​+1)﻿ .

﻿25x52+4x2+c\frac{2}{5}x^{\frac{5}{2}}+4x^2+c52​x25​+4x2+c﻿

﻿23x32+2x12+c\frac{2}{3}x^{\frac{3}{2}}+2x^{\frac{1}{2}}+c32​x23​+2x21​+c﻿

﻿25x52+12x12+c\frac{2}{5}x^{\frac{5}{2}}+\frac{1}{2}x^{\frac{1}{2}}+c52​x25​+21​x21​+c﻿

What is the antiderivative of ﻿f(x)=6x2f\left(x\right)=6x^2f(x)=6x2﻿ .

﻿4x2+c4x^2+c4x2+c﻿

﻿6x2+c6x^2+c6x2+c﻿

﻿2x3+c2x^3+c2x3+c﻿

What is the antiderivative of ﻿f(x)=(x+1)x12f\left(x\right)=\frac{\left(x+1\right)}{x^{\frac{1}{2}}}f(x)=x21​(x+1)​﻿ .

(2x+3)3/2 + c

﻿23x32+2x12+c\frac{2}{3}x^{\frac{3}{2}}+2x^{\frac{1}{2}}+c32​x23​+2x21​+c﻿

(2x+3)1/2 + c

What is the antiderivative of ﻿f(x)=(1−x12)2xf\left(x\right)=\frac{\left(1-x^{\frac{1}{2}}\right)^2}{\sqrt{x}}f(x)=x​(1−x21​)2​﻿ .

﻿(2x+3)32+c\left(2x+3\right)^{\frac{3}{2}}+c(2x+3)23​+c﻿

﻿23x32+2x12+c\frac{2}{3}x^{\frac{3}{2}}+2x^{\frac{1}{2}}+c32​x23​+2x21​+c﻿

﻿2x12+23x32−2x+c2x^{\frac{1}{2}}+\frac{2}{3}x^{\frac{3}{2}}-2x+c2x21​+32​x23​−2x+c﻿

What is the antiderivative of ﻿f(x)=6x2f\left(x\right)=6x^2f(x)=6x2﻿ .

﻿x3−x2+x+cx^3-x^2+x+cx3−x2+x+c﻿

﻿6x2+2x+c6x^2+2x+c6x2+2x+c﻿

﻿2x3−x+c2x^3-x+c2x3−x+c﻿

What is the antiderivative of ﻿f(x)=1xf\left(x\right)=\frac{1}{x}f(x)=x1​﻿ .

﻿ln⁡(2x2)+c\ln\left(2x^2\right)+cln(2x2)+c﻿

﻿ln⁡(2x)+c\ln\left(2x^{ }\right)+cln(2x)+c﻿

﻿ln⁡(x)+c\ln\left(x^{ }\right)+cln(x)+c﻿

What is the antiderivative of ﻿f(x)=3x2−2x+1f\left(x\right)=3x^2-2x+1f(x)=3x2−2x+1﻿ .

﻿4x2+c4x^2+c4x2+c﻿

﻿6x2+c6x^2+c6x2+c﻿

﻿2x3+c2x^3+c2x3+c﻿

What is the antiderivative of ﻿f(x)=x+1xf\left(x\right)=\sqrt{x}+\frac{1}{\sqrt{x}}f(x)=x​+x​1​﻿ .

﻿﻿25x52+4x2+c\frac{2}{5}x^{\frac{5}{2}}+4x^2+c52​x25​+4x2+c﻿

﻿23x52+2x12+c\frac{2}{3}x^{\frac{5}{2}}+2x^{\frac{1}{2}}+c32​x25​+2x21​+c﻿

﻿25x52+12x2+c\frac{2}{5}x^{\frac{5}{2}}+\frac{1}{2}x^2+c52​x25​+21​x2+c﻿

What is the antiderivative of ﻿f(x)=exf\left(x\right)=e^xf(x)=ex﻿ .

﻿ln⁡(exx2)+c\ln\left(e^xx^2\right)+cln(exx2)+c﻿

﻿ex+ce^x+cex+c﻿

﻿2ex+c2e^x+c2ex+c﻿

What is the antiderivative of ﻿f(x)=xf\left(x\right)=\sqrt{x}f(x)=x​﻿ .

﻿25x52+4x2+c\frac{2}{5}x^{\frac{5}{2}}+4x^2+c52​x25​+4x2+c﻿

﻿25x52+c\frac{2}{5}x^{\frac{5}{2}}+c52​x25​+c﻿

﻿23x32+c\frac{2}{3}x^{\frac{3}{2}}+c32​x23​+c﻿

Incorrect

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What is the antiderivative of $f\left(x\right)=x\left(\sqrt{x\ }+1\right)$ .

$\frac{2}{5}x^{\frac{5}{2}}+4x^2+c$

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

$\frac{2}{5}x^{\frac{5}{2}}+\frac{1}{2}x^{\frac{1}{2}}+c$

What is the antiderivative of $f\left(x\right)=6x^2$ .

$4x^2+c$

$6x^2+c$

$2x^3+c$

What is the antiderivative of $f\left(x\right)=\frac{\left(x+1\right)}{x^{\frac{1}{2}}}$ .

(2x+3)^3/2+ c

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

(2x+3)^1/2+ c

What is the antiderivative of $f\left(x\right)=\frac{\left(1-x^{\frac{1}{2}}\right)^2}{\sqrt{x}}$ .

$\left(2x+3\right)^{\frac{3}{2}}+c$

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

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

What is the antiderivative of $f\left(x\right)=6x^2$ .

$x^3-x^2+x+c$

$6x^2+2x+c$

$2x^3-x+c$

What is the antiderivative of $f\left(x\right)=\frac{1}{x}$ .

$\ln\left(2x^2\right)+c$

$\ln\left(2x^{ }\right)+c$

$\ln\left(x^{ }\right)+c$

What is the antiderivative of $f\left(x\right)=3x^2-2x+1$ .

$4x^2+c$

$6x^2+c$

$2x^3+c$

What is the antiderivative of $f\left(x\right)=\sqrt{x}+\frac{1}{\sqrt{x}}$ .

$\frac{2}{5}x^{\frac{5}{2}}+4x^2+c$

$\frac{2}{3}x^{\frac{5}{2}}+2x^{\frac{1}{2}}+c$

$\frac{2}{5}x^{\frac{5}{2}}+\frac{1}{2}x^2+c$

What is the antiderivative of $f\left(x\right)=e^x$ .

$\ln\left(e^xx^2\right)+c$

$e^x+c$

$2e^x+c$

What is the antiderivative of $f\left(x\right)=\sqrt{x}$ .

$\frac{2}{5}x^{\frac{5}{2}}+4x^2+c$

$\frac{2}{5}x^{\frac{5}{2}}+c$

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