Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
46401	Find the Antiderivative	square root of natural log of x	$\sqrt{\ln (x)}$
46402	Find the Antiderivative	11x^10	$11 x^{10}$
46403	Find the Roots (Zeros)	2x^3+3x^2-12x+6	$2 x^{3} + 3 x^{2} - 12 x + 6$
46404	Find the Roots (Zeros)	3x^2+26x-9	$3 x^{2} + 26 x - 9$
46405	Find the Roots (Zeros)	(x^3+7x^2-9x-63)÷(x+3)	$(x^{3} + 7 x^{2} - 9 x - 63) \div (x + 3)$
46406	Find the Roots (Zeros)	-(576x)/((16x^2-9)^2)	$- \frac{576 x}{{(16 x^{2} - 9)}^{2}}$
46407	Find the Roots (Zeros)	x^2+6x-7	$x^{2} + 6 x - 7$
46408	Find the Roots (Zeros)	3x^2-16x+5	$3 x^{2} - 16 x + 5$
46409	Find the Roots (Zeros)	36x^2-120x+84	$36 x^{2} - 120 x + 84$
46410	Find the Roots (Zeros)	2x^2-18	$2 x^{2} - 18$
46411	Find the Roots (Zeros)	x^3-43x+42	$x^{3} - 43 x + 42$
46412	Find the Roots (Zeros)	x+2sin(x)	$x + 2 \sin (x)$
46413	Find the Roots (Zeros)	x^2-13x+40	$x^{2} - 13 x + 40$
46414	Find the Roots (Zeros)	3x^2-2x-5	$3 x^{2} - 2 x - 5$
46415	Find the Roots (Zeros)	-(1600x)/((25x^2-16)^2)	$- \frac{1600 x}{{(25 x^{2} - 16)}^{2}}$
46416	Find the Roots (Zeros)	6x^2+66x+168	$6 x^{2} + 66 x + 168$
46417	Find the Roots (Zeros)	x^3-cos(x)	$x^{3} - \cos (x)$
46418	Find the Roots (Zeros)	12x^2-156x+350	$12 x^{2} - 156 x + 350$
46419	Find the Roots (Zeros)	3x^2-16x	$3 x^{2} - 16 x$
46420	Find the Roots (Zeros)	x^4+55x^2-576	$x^{4} + 55 x^{2} - 576$
46421	Find the Roots (Zeros)	x^4-3x^3+2x^2	$x^{4} - 3 x^{3} + 2 x^{2}$
46422	Find the Roots (Zeros)	x^2+10x+22	$x^{2} + 10 x + 22$
46423	Find the Roots (Zeros)	12x^3-60x^2+84x-36	$12 x^{3} - 60 x^{2} + 84 x - 36$
46424	Find the Roots (Zeros)	6x^2-78x+240	$6 x^{2} - 78 x + 240$
46425	Find the Roots (Zeros)	2/(x^(1/3))-2	$\frac{2}{x^{\frac{1}{3}}} - 2$
46426	Find the Roots (Zeros)	-3x^3+40x^2-144x+128	$- 3 x^{3} + 40 x^{2} - 144 x + 128$
46427	Find the Antiderivative	4cos(x)^2	$4 \cos^{2} (x)$
46428	Find the Antiderivative	x^2e^x+2xe^x	$x^{2} e^{x} + 2 x e^{x}$
46429	Find the Antiderivative	4 natural log of x	$4 \ln (x)$
46430	Find the Antiderivative	x/6	$\frac{x}{6}$
46431	Find the Antiderivative	12cos(2x)^3	$12 \cos^{3} (2 x)$
46432	Find the Antiderivative	1/(x^2)+4x	$\frac{1}{x^{2}} + 4 x$
46433	Find the Antiderivative	pisin(pix)	$π \sin (π x)$
46434	Find the Antiderivative	12sin(x)	$12 \sin (x)$
46435	Find the Antiderivative	(e^(tan(x)))/(cos(x)^2)	$\frac{e^{\tan (x)}}{\cos^{2} (x)}$
46436	Find the Antiderivative	15x^14	$15 x^{14}$
46437	Find the Antiderivative	(x+6)(3x-4)	$(x + 6) (3 x - 4)$
46438	Find the Antiderivative	sec(2x)	$\sec (2 x)$
46439	Find the Antiderivative	e^(-5t)	$e^{- 5 t}$
46440	Find the Antiderivative	(x^2+1)/( square root of x)	$\frac{(x^{2} + 1)}{\sqrt{x}}$
46441	Find the Antiderivative	-2x+4	$- 2 x + 4$
46442	Find the Antiderivative	e^(5x^2)	$e^{5 x^{2}}$
46443	Find the Antiderivative	-5e^x	$- 5 e^{x}$
46444	Find the Antiderivative	12/(x^5)	$\frac{12}{x^{5}}$
46445	Find the Antiderivative	(x+1)/x	$\frac{(x + 1)}{x}$
46446	Find the Antiderivative	x^3+5x^2+6x	$x^{3} + 5 x^{2} + 6 x$
46447	Find the Antiderivative	3 natural log of x	$3 \ln (x)$
46448	Find the Antiderivative	-e^(-t)	$- e^{- t}$
46449	Find the Antiderivative	16sin(2x)^2	$16 \sin^{2} (2 x)$
46450	Find the Antiderivative	(y^3)/2	$\frac{y^{3}}{2}$
46451	Find the Antiderivative	1/((x+1)^3)	$\frac{1}{{(x + 1)}^{3}}$
46452	Find the Antiderivative	210sin(17.5t)	$210 \sin (17.5 t)$
46453	Find the Antiderivative	1-cos(2x)	$1 - \cos (2 x)$
46454	Find the Antiderivative	sin((pix)/2)	$\sin (\frac{π x}{2})$
46455	Find the Antiderivative	8x^3-12x	$8 x^{3} - 12 x$
46456	Find the Antiderivative	(5/3)^x	${(\frac{5}{3})}^{x}$
46457	Find the Antiderivative	x^(-1/4)	$x^{- \frac{1}{4}}$
46458	Find the Antiderivative	(y+3)y^2	$(y + 3) y^{2}$
46459	Find the Antiderivative	(cos( square root of x))/( square root of x)	$\frac{\cos (\sqrt{x})}{\sqrt{x}}$
46460	Find the Antiderivative	(x-3)/( square root of x)	$\frac{x - 3}{\sqrt{x}}$
46461	Find the Antiderivative	(x^2+x+1)/x	$\frac{x^{2} + x + 1}{x}$
46462	Find the Antiderivative	-7x^-8	$- 7 x^{- 8}$
46463	Find the Antiderivative	sin(10x)	$\sin (10 x)$
46464	Find the Antiderivative	8x+1	$8 x + 1$
46465	Find the Antiderivative	square root of cos(x)	$\sqrt{\cos (x)}$
46466	Find the Antiderivative	sec(3x)^2	$\sec^{2} (3 x)$
46467	Find the Antiderivative	e^(-8t)	$e^{- 8 t}$
46468	Find the Antiderivative	5 natural log of x	$5 \ln (x)$
46469	Find the Antiderivative	20sin((x^2)/35)	$20 \sin (\frac{x^{2}}{35})$
46470	Find the Area Between the Curves	y=4/x , y=16x , y=1/4x , x>0	$y = \frac{4}{x}$ , $y = 16 x$ , $y = \frac{1}{4} x$ , $x > 0$
46471	Find the Area Between the Curves	y=14-x^2 , y=x^2-4	$y = 14 - x^{2}$ , $y = x^{2} - 4$
46472	Find the Area Between the Curves	y = square root of x+2 , y=1/(x+1) , x=2	$y = \sqrt{x + 2}$ , $y = \frac{1}{x + 1}$ , $x = 2$
46473	Find the Area Between the Curves	x=y^2 , x=2y	$x = y^{2}$ , $x = 2 y$
46474	Find the Area Between the Curves	x=45-5y^2 , x=5y^2-45	$x = 45 - 5 y^{2}$ , $x = 5 y^{2} - 45$
46475	Find the Area Between the Curves	y=x^2 , y^2=x	$y = x^{2}$ , $y^{2} = x$
46476	Find the Domain and Range	y=tan(theta)	$y = \tan (θ)$
46477	Find the Domain and Range	y=arccos(cos(x))	$y = \arccos (\cos (x))$
46478	Find the Concavity	x^3+12x+1	$x^{3} + 12 x + 1$
46479	Find the Concavity	(x+9)/(x^2-81)	$\frac{x + 9}{x^{2} - 81}$
46480	Find Where Undefined/Discontinuous	(x^2-3x+2)/(x^2-2x)	$\frac{x^{2} - 3 x + 2}{x^{2} - 2 x}$
46481	Find the Average Rate of Change	f(x)=cot(x) , [pi/4,(3pi)/4]	$f (x) = \cot (x)$ , $[\frac{π}{4}, \frac{3 π}{4}]$
46482	Find the Concavity	x^3-9x^2+25x-21	$x^{3} - 9 x^{2} + 25 x - 21$
46483	Find the Concavity	natural log of x^2-4x+13	$\ln (x^{2} - 4 x + 13)$
46484	Find the Concavity	6sin(x)+6cos(x)	$6 \sin (x) + 6 \cos (x)$
46485	Find the Concavity	3x^4-6x^3+x-5	$3 x^{4} - 6 x^{3} + x - 5$
46486	Find the Tangent Line at (0,p)	sin(y)=x ; (0,pi)	$\sin (y) = x$ ; $(0, π)$
46487	Find the Tangent Line at (0,0)	y=sin(2x)+sin(2x)^2 , (0,0)	$y = \sin (2 x) + \sin^{2} (2 x)$ , $(0, 0)$
46488	Find the Tangent Line at (1,5)	y=6x^2-x^3 , (1,5)	$y = 6 x^{2} - x^{3}$ , $(1, 5)$
46489	Find the Tangent Line at (p/2,2p)	y=4xsin(x) , (pi/2,2pi)	$y = 4 x \sin (x)$ , $(\frac{π}{2}, 2 π)$
46490	Find the Tangent Line at (5,p/8)	y=1/2arctan(1/5x) , (5,pi/8)	$y = \frac{1}{2} \arctan (\frac{1}{5} x)$ , $(5, \frac{π}{8})$
46491	Find the Tangent Line at (2,4)	y=x^3-3x+2 , (2,4)	$y = x^{3} - 3 x + 2$ , $(2, 4)$
46492	Find the Tangent Line at (0,0)	y=sin(6x)+sin(6x)^2 , (0,0)	$y = \sin (6 x) + \sin^{2} (6 x)$ , $(0, 0)$
46493	Find the Tangent Line at (1,8)	y=x^4+8x^2-x , (1,8)	$y = x^{4} + 8 x^{2} - x$ , $(1, 8)$
46494	Find the Tangent Line at (1,9)	y=x^4+9x^2-x , (1,9)	$y = x^{4} + 9 x^{2} - x$ , $(1, 9)$
46495	Find the Tangent Line at (1,-1)	(x-y-1)^3=x ; (1,-1)	${(x - y - 1)}^{3} = x$ ; $(1, - 1)$
46496	Find the Tangent Line at (4,8)	y=4 square root of x , (4,8)	$y = 4 \sqrt{x}$ , $(4, 8)$
46497	Find the Tangent Line at (16,64)	y=16 square root of x , (16,64)	$y = 16 \sqrt{x}$ , $(16, 64)$
46498	Find the Tangent Line at (0,9)	y=x^4+9e^x , (0,9)	$y = x^{4} + 9 e^{x}$ , $(0, 9)$
46499	Find the Linearization at a=p/2	f(x)=cos(x) , a=pi/2	$f (x) = \cos (x)$ , $a = \frac{π}{2}$
46500	Find the Linearization at a=1	f(x)=x+1/x , a=1	$f (x) = x + \frac{1}{x}$ , $a = 1$