Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
81201	Find the Concavity	f(x)=1/3x^3-3x^2-16x	$f (x) = \frac{1}{3} x^{3} - 3 x^{2} - 16 x$
81202	Evaluate the Integral	integral from e to 4 of 1/(x natural log of x) with respect to x	$\int_{e}^{4} \frac{1}{x \ln (x)} d x$
81203	Evaluate the Integral	integral of 1/(2 square root of x^3) with respect to x	$\int \frac{1}{2 \sqrt{x^{3}}} d x$
81204	Evaluate the Limit	limit as x approaches 0 of (x^2-3x)/(2x^2-9x)	$lim_{x \to 0} \frac{x^{2} - 3 x}{2 x^{2} - 9 x}$
81205	Find the Derivative - d/dx	sinh(2x)	$\sinh (2 x)$
81206	Evaluate the Limit	limit as x approaches negative infinity of ( square root of x+3x^2)/(-4x+1)	$lim_{x \to - \infty} \frac{\sqrt{x + 3 x^{2}}}{- 4 x + 1}$
81207	Find dx/dy	xy+y^2=1	$x y + y^{2} = 1$
81208	Find the Antiderivative	cube root of x+1	$\sqrt[3]{x + 1}$
81209	Find the Antiderivative	(x+ square root of x+1)/( cube root of x)	$\frac{x + \sqrt{x} + 1}{\sqrt[3]{x}}$
81210	Find the Inflection Points	f(x)=2/15x^6+x^5-8x^4	$f (x) = \frac{2}{15} x^{6} + x^{5} - 8 x^{4}$
81211	Find the Integral	(x^2)/(x+1)	$\frac{x^{2}}{x + 1}$
81212	Evaluate the Limit	limit as x approaches 0 of (e^(2x)-1)/(3e^x-3)	$lim_{x \to 0} \frac{e^{2 x} - 1}{3 e^{x} - 3}$
81213	Find the Inflection Points	1/6x^6+x^5-5x^4	$\frac{1}{6} x^{6} + x^{5} - 5 x^{4}$
81214	Find the Antiderivative	f(x)=1/((5x-1)^4)	$f (x) = \frac{1}{{(5 x - 1)}^{4}}$
81215	Find dy/dx	-3y-1-y^3-x^3=-y^2	$- 3 y - 1 - y^{3} - x^{3} = - y^{2}$
81216	Find the Antiderivative	f(x)=15x^4+x	$f (x) = 15 x^{4} + x$
81217	Find the Derivative - d/dx	e^(-x)+e^(2x)	$e^{- x} + e^{2 x}$
81218	Find the Derivative - d/dx	arctanh(e^x)	$arctanh (e^{x})$
81219	Find dY/dx	Y=x^-2	$Y = x^{- 2}$
81220	Find the Antiderivative	((x^2-1)^2)/(x^2)	$\frac{{(x^{2} - 1)}^{2}}{x^{2}}$
81221	Evaluate the Integral	integral of (2x^2-3)/( square root of x) with respect to x	$\int \frac{2 x^{2} - 3}{\sqrt{x}} d x$
81222	Find dy/dx	x^2+2x^3+3y^2-4y^3=-x	$x^{2} + 2 x^{3} + 3 y^{2} - 4 y^{3} = - x$
81223	Evaluate the Integral	integral of (8x^3+1/(2x^2)) with respect to x	$\int (8 x^{3} + \frac{1}{2 x^{2}}) d x$
81224	Evaluate the Limit	limit as x approaches -2 of (x^3+5x^2+6x)/(x^2(x+2)-(x+2))	$lim_{x \to - 2} \frac{x^{3} + 5 x^{2} + 6 x}{x^{2} (x + 2) - (x + 2)}$
81225	Evaluate the Limit	limit as x approaches 2 of ( square root of 2x+5)/(1-3x)	$lim_{x \to 2} \frac{\sqrt{2 x + 5}}{1 - 3 x}$
81226	Find the Antiderivative	f(x)=-1/((6x+1)^2)	$f (x) = - \frac{1}{{(6 x + 1)}^{2}}$
81227	Find the Derivative - d/dx	y=arccos(3x-5)	$y = \arccos (3 x - 5)$
81228	Evaluate the Integral	integral of 1/(x square root of x^4-1) with respect to x	$\int \frac{1}{x \sqrt{x^{4} - 1}} d x$
81229	Find the Concavity	f(x)=1/4x^4+4x^3+24x^2	$f (x) = \frac{1}{4} x^{4} + 4 x^{3} + 24 x^{2}$
81230	Evaluate the Integral	integral from 0 to 1 of (1+4x+9x^2+16x^3) with respect to x	$\int_{0}^{1} (1 + 4 x + 9 x^{2} + 16 x^{3}) d x$
81231	Find the Derivative - d/dx	sin(x^2+pi)	$\sin (x^{2} + π)$
81232	Find dy/dx	10x^3+5y^2=25y	$10 x^{3} + 5 y^{2} = 25 y$
81233	Find dy/dx	3y^2-4x=x^2y	$3 y^{2} - 4 x = x^{2} y$
81234	Evaluate the Integral	integral from e to e^2 of natural log of x with respect to x	$\int_{e}^{e^{2}} \ln (x) d x$
81235	Find dy/dx	-4x-5y^3+4-x^2=0	$- 4 x - 5 y^{3} + 4 - x^{2} = 0$
81236	Use Logarithmic Differentiation to Find the Derivative	y=x^4sin(x)	$y = x^{4} \sin (x)$
81237	Evaluate the Limit	limit as x approaches 9 of (2x^2-162)/(x+3 square root of x-18)	$lim_{x \to 9} \frac{2 x^{2} - 162}{x + 3 \sqrt{x} - 18}$
81238	Find dy/dx	y=3^(4x)	$y = 3^{4 x}$
81239	Find the Antiderivative	f(x)=x^2e^x	$f (x) = x^{2} e^{x}$
81240	Evaluate the Summation	sum from i=1 to 50 of (5i-2)(i+3)	$\sum_{i = 1}^{50} (5 i - 2) (i + 3)$
81241	Integrate Using u-Substitution	integral of sin(x)^3cos(x) with respect to x	$\int \sin^{3} (x) \cos (x) d x$
81242	Find the Antiderivative	f(x)=5e^x-2x^4	$f (x) = 5 e^{x} - 2 x^{4}$
81243	Find dy/dx	y=arcsin(1/( square root of x))	$y = \arcsin (\frac{1}{\sqrt{x}})$
81244	Find the Second Derivative	y=(2x)/3+(3x)/2	$y = \frac{2 x}{3} + \frac{3 x}{2}$
81245	Find the Antiderivative	f(x)=7x(x-1)^6	$f (x) = 7 x {(x - 1)}^{6}$
81246	Find the Derivative - d/dx	(2x)/(e^(2x))	$\frac{2 x}{e^{2 x}}$
81247	Find the Slope of the Tangent Line at (9,3)	y = square root of x , (9,3)	$y = \sqrt{x}$ , $(9, 3)$
81248	Find the Concavity	f(x)=1/6x^4+x^3-18x^2	$f (x) = \frac{1}{6} x^{4} + x^{3} - 18 x^{2}$
81249	Find dx/dy	y=(5x-1)^(1/3)	$y = {(5 x - 1)}^{\frac{1}{3}}$
81250	Evaluate the Integral	integral of (sin(x))(1/(cos(x))+csc(x)) with respect to x	$\int (\sin (x)) (\frac{1}{\cos (x)} + \csc (x)) d x$
81251	Find dy/dx	y=x+3 natural log of 5x-4x^2+e^(2x)-pi	$y = x + 3 \ln (5 x) - 4 x^{2} + e^{2 x} - π$
81252	Find the Maximum/Minimum Value	f(x)=1/3x^3-x^2-3x+4	$f (x) = \frac{1}{3} x^{3} - x^{2} - 3 x + 4$
81253	Find the Antiderivative	1/(cos(2x)^2)	$\frac{1}{\cos^{2} (2 x)}$
81254	Find dy/dx	-2y=-5x^2-4x+3y^3	$- 2 y = - 5 x^{2} - 4 x + 3 y^{3}$
81255	Find the Maximum/Minimum Value	y=3x-x^3	$y = 3 x - x^{3}$
81256	Find dy/dx	-3-4x^3=2y+xy	$- 3 - 4 x^{3} = 2 y + x y$
81257	Find the Antiderivative	cos(x)^2*sin(x)	$\cos^{2} (x) \cdot \sin (x)$
81258	Evaluate the Limit	limit as x approaches 0 of x/( square root of 1+x- square root of 1-x)	$lim_{x \to 0} \frac{x}{\sqrt{1 + x} - \sqrt{1 - x}}$
81259	Find the Average Value of the Function	f(x)=3/x , [1,7]	$f (x) = \frac{3}{x}$ , $[1, 7]$
81260	Evaluate the Limit	limit as x approaches pi/((2)^(-)) of tan(x)	$lim_{x \to \frac{π}{{(2)}^{-}}} \tan (x)$
81261	Find dy/dx	-xy=4-5y^3	$- x y = 4 - 5 y^{3}$
81262	Find dy/dx	-4+2y^2+2x^2+5y^3=0	$- 4 + 2 y^{2} + 2 x^{2} + 5 y^{3} = 0$
81263	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (2-e^(x/2))^(4/x)	$lim_{x \to 0} {(2 - e^{\frac{x}{2}})}^{\frac{4}{x}}$
81264	Evaluate the Limit	limit as x approaches 3 of x^4+x^3-4x^2-2x+1	$lim_{x \to 3} x^{4} + x^{3} - 4 x^{2} - 2 x + 1$
81265	Find the Antiderivative	cos(x)sin(x)	$\cos (x) \sin (x)$
81266	Evaluate the Integral	integral of (2x^2e^(5x^3+1))/(3-e^(5x^3+1)) with respect to x	$\int \frac{2 x^{2} e^{5 x^{3} + 1}}{3 - e^{5 x^{3} + 1}} d x$
81267	Evaluate the Limit	limit as x approaches -1 of (x^3+3x^2+3x+1)/((x+1)^2)	$lim_{x \to - 1} \frac{x^{3} + 3 x^{2} + 3 x + 1}{{(x + 1)}^{2}}$
81268	Evaluate the Integral	integral of ( cube root of x)^4 with respect to x	$\int {(\sqrt[3]{x})}^{4} d x$
81269	Evaluate the Integral	integral of fifth root of 1+7x with respect to x	$\int \sqrt[5]{1 + 7 x} d x$
81270	Evaluate the Integral	integral of 2+x^3+x^6 with respect to x	$\int 2 + x^{3} + x^{6} d x$
81271	Evaluate the Limit	limit as x approaches 0 of (6xe^(-3x+9))/(6x^2+x)	$lim_{x \to 0} \frac{6 x e^{- 3 x + 9}}{6 x^{2} + x}$
81272	Find the Derivative - d/dx	d/(dx)(4sin(3x))+ integral of 5sin(2x) with respect to x	$\frac{d}{d x} (4 \sin (3 x)) + \int 5 \sin (2 x) d x$
81273	Find the Antiderivative	(x+1)/(x^2)	$\frac{x + 1}{x^{2}}$
81274	Evaluate the Integral	integral of ( sixth root of x)^3 with respect to x	$\int {(\sqrt[6]{x})}^{3} d x$
81275	Find the Derivative - d/dh	- square root of 5h	$- \sqrt{5 h}$
81276	Find the Antiderivative	2^(x+1)	$2^{x + 1}$
81277	Evaluate the Integral	integral of x(3x-4)(4x+3) with respect to x	$\int x (3 x - 4) (4 x + 3) d x$
81278	Evaluate the Limit	limit as x approaches 0 of (6e^(4x)-2e^(3x)-4)/(sin(2x))	$lim_{x \to 0} \frac{6 e^{4 x} - 2 e^{3 x} - 4}{\sin (2 x)}$
81279	Integrate Using u-Substitution	integral of x^2cos(x^3) with respect to x	$\int x^{2} \cos (x^{3}) d x$
81280	Evaluate the Summation	4 sum from i=0 to 3 of 1+2i^2	$4 \sum_{i = 0}^{3} 1 + 2 i^{2}$
81281	Find the Derivative - d/dx	(1+x+y)/( square root of 1+x^2+y^2)	$\frac{1 + x + y}{\sqrt{1 + x^{2} + y^{2}}}$
81282	Evaluate the Integral	integral of ((2x-5)^2)/( square root of x) with respect to x	$\int \frac{{(2 x - 5)}^{2}}{\sqrt{x}} d x$
81283	Evaluate the Integral	integral from e^64 to e^81 of 1/(x square root of natural log of x) with respect to x	$\int_{e^{64}}^{e^{81}} \frac{1}{x \sqrt{\ln (x)}} d x$
81284	Evaluate the Limit	limit as x approaches c of (8)^(2/3)	$lim_{x \to c} {(8)}^{\frac{2}{3}}$
81285	Evaluate the Limit	limit as x approaches -4 from the right of square root of 5x+20-8	$lim_{x \to {(- 4)}^{+}} \sqrt{5 x + 20} - 8$
81286	Find the Maximum/Minimum Value	y=x^3+3x^2	$y = x^{3} + 3 x^{2}$
81287	Find dy/dx	y=(2x-1)(3x+5)	$y = (2 x - 1) (3 x + 5)$
81288	Find the Derivative - d/dx	1/(2 square root of x+1)	$\frac{1}{2 \sqrt{x + 1}}$
81289	Find the Concavity	f(x)=-1/6x^4+4x^3-36x^2	$f (x) = - \frac{1}{6} x^{4} + 4 x^{3} - 36 x^{2}$
81290	Find the Antiderivative	(3x-2)/((x-2)^2)	$\frac{3 x - 2}{{(x - 2)}^{2}}$
81291	Find dy/dx	2xy^3-x^3=y^2	$2 x y^{3} - x^{3} = y^{2}$
81292	Evaluate the Integral	integral from 1 to 2 of 2x square root of 4+x^2 with respect to x	$\int_{1}^{2} 2 x \sqrt{4 + x^{2}} d x$
81293	Evaluate the Integral	integral of 8^(2y^3-3y^2)(y^2-y) with respect to y	$\int 8^{2 y^{3} - 3 y^{2}} (y^{2} - y) d y$
81294	Find the Antiderivative	natural log of xdx	$\ln (x d x)$
81295	Find Where Increasing/Decreasing	-2x^4-16x^3-32x^2	$- 2 x^{4} - 16 x^{3} - 32 x^{2}$
81296	Find the Derivative - d/dx	2e^( square root of x)	$2 e^{\sqrt{x}}$
81297	Integrate By Parts	integral from 0 to 1 of (x^2+1)e^(-x) with respect to x	$\int_{0}^{1} (x^{2} + 1) e^{- x} d x$
81298	Find the Derivative - d/dx	y=4/(x^2-3x+2)	$y = \frac{4}{x^{2} - 3 x + 2}$
81299	Evaluate the Integral	integral of (12x^-6+17/(3x)) with respect to x	$\int (12 x^{- 6} + \frac{17}{3 x}) d x$
81300	Find dy/dx	3y+2x^2=-xy	$3 y + 2 x^{2} = - x y$