Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
81301	Find the Inflection Points	1/5x^5-x^4-12x^3	$\frac{1}{5} x^{5} - x^{4} - 12 x^{3}$
81302	Find the Integral	1/(x^2+2)	$\frac{1}{x^{2} + 2}$
81303	Evaluate the Integral	integral from 0 to 1 of ( natural log of x)/x with respect to x	$\int_{0}^{1} \frac{\ln (x)}{x} d x$
81304	Integrate Using u-Substitution	integral of tan(x)^2sec(x)^2 with respect to x	$\int \tan^{2} (x) \sec^{2} (x) d x$
81305	Evaluate the Limit	limit as x approaches infinity of ((x+1)(5x-3))/(x^2+3)	$lim_{x \to \infty} \frac{(x + 1) (5 x - 3)}{x^{2} + 3}$
81306	Find the Antiderivative	(x-1)/(x+2)	$\frac{x - 1}{x + 2}$
81307	Integrate Using u-Substitution	integral of tan(x)sec(x)^2 with respect to x	$\int \tan (x) \sec^{2} (x) d x$
81308	Find the Maximum/Minimum Value	y=6sin(pix-6)-6	$y = 6 \sin (π x - 6) - 6$
81309	Find the Antiderivative	1/(x(x-3))	$\frac{1}{x (x - 3)}$
81310	Find the Derivative - d/dx	\|x\|-3\|x+1\|	$\| x \| - 3 \| x + 1 \|$
81311	Find dy/dx	y=arctan(sin(x^2-6x))	$y = \arctan (\sin (x^{2} - 6 x))$
81312	Find the Antiderivative	e^x+e^(-x)	$e^{x} + e^{- x}$
81313	Find the Maximum/Minimum Value	f(x)=x^(2/3)	$f (x) = x^{\frac{2}{3}}$
81314	Find the Derivative - d/dx	y=arccoth(cosh(x))	$y = arccoth (\cosh (x))$
81315	Eliminate the Parameter	x=9t^2 and y=27t^3	$x = 9 t^{2}$ and $y = 27 t^{3}$
81316	Find dx/dy	x^2y+xy^2=3x	$x^{2} y + x y^{2} = 3 x$
81317	Integrate Using u-Substitution	integral of cos(x)^3sin(x) with respect to x	$\int \cos^{3} (x) \sin (x) d x$
81318	Evaluate the Limit	limit as x approaches -2 of 1/(\|x+2\|)+x^2	$lim_{x \to - 2} \frac{1}{\| x + 2 \|} + x^{2}$
81319	Integrate Using u-Substitution	integral of 5/(x^2) with respect to x	$\int \frac{5}{x^{2}} d x$
81320	Find the Derivative - d/dx	x+ natural log of x	$x + \ln (x)$
81321	Find Where Increasing/Decreasing	f(x)=x^4+x^3-4x^2+5	$f (x) = x^{4} + x^{3} - 4 x^{2} + 5$
81322	Find dy/dx	3xy=4x+y^2	$3 x y = 4 x + y^{2}$
81323	Evaluate the Limit	limit as n approaches infinity of (6n^3+2n^2+10)/(n^3+1)	$lim_{n \to \infty} \frac{6 n^{3} + 2 n^{2} + 10}{n^{3} + 1}$
81324	Evaluate the Limit	limit as x approaches 5 of (5- square root of 6-x)/x	$lim_{x \to 5} \frac{5 - \sqrt{6 - x}}{x}$
81325	Evaluate the Limit	limit as x approaches infinity of (e^x)/(x^4)	$lim_{x \to \infty} \frac{e^{x}}{x^{4}}$
81326	Find dy/dx	y-2x^2=xy-5	$y - 2 x^{2} = x y - 5$
81327	Evaluate the Limit	limit as x approaches 0 of (3x^2-6x)/(6x^2+2x)	$lim_{x \to 0} \frac{3 x^{2} - 6 x}{6 x^{2} + 2 x}$
81328	Find the Absolute Max and Min over the Interval	5+2i	$5 + 2 i$
81329	Find the Derivative - d/dx	y = cube root of x^2(2e^x-x^2)	$y = \sqrt[3]{x^{2}} (2 e^{x} - x^{2})$
81330	Find the Second Derivative	f(x)=(x^2-1)/x	$f (x) = \frac{x^{2} - 1}{x}$
81331	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (2-15e^(-5x))/(1/x+4cos(5/x))	$lim_{x \to \infty} \frac{2 - 15 e^{- 5 x}}{\frac{1}{x} + 4 \cos (\frac{5}{x})}$
81332	Integrate Using u-Substitution	integral of 1/(5-3x) with respect to x	$\int \frac{1}{5 - 3 x} d x$
81333	Evaluate the Limit	limit as x approaches -1/2 of 4x(3x+4)^2	$lim_{x \to - \frac{1}{2}} 4 x {(3 x + 4)}^{2}$
81334	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^(-x)-1)/(sin(3x)-3x)	$lim_{x \to 0} \frac{e^{- x} - 1}{\sin (3 x) - 3 x}$
81335	Find the Concavity	f(x)=-3/20x^5-2x^4-8x^3	$f (x) = - \frac{3}{20} x^{5} - 2 x^{4} - 8 x^{3}$
81336	Find dy/dx	-xy+5-5y^2=3x^3	$- x y + 5 - 5 y^{2} = 3 x^{3}$
81337	Evaluate the Integral	integral from 0 to 1 of (1/(x+1)+1/((x+4)^2)) with respect to x	$\int_{0}^{1} (\frac{1}{x + 1} + \frac{1}{{(x + 4)}^{2}}) d x$
81338	Evaluate the Limit	limit as x approaches 1 of ((x^2-4x^2)/(x^2+x-2))^3	$lim_{x \to 1} {(\frac{x^{2} - 4 x^{2}}{x^{2} + x - 2})}^{3}$
81339	Find the Derivative - d/dx	4x^2(3x^3-2x^2+5x)	$4 x^{2} (3 x^{3} - 2 x^{2} + 5 x)$
81340	Find the Area Under the Curve	f(x)=x^2+4x+4 , [-4,2] , n=7	$f (x) = x^{2} + 4 x + 4$ , $[- 4, 2]$ , $n = 7$
81341	Find dy/dx	y^3+x^2+5=4y^2	$y^{3} + x^{2} + 5 = 4 y^{2}$
81342	Find the Derivative - d/dx	log of x+1	$\log (x + 1)$
81343	Find the Antiderivative	2x square root of x	$2 x \sqrt{x}$
81344	Integrate Using u-Substitution	integral of cos(x)^3 with respect to x	$\int \cos^{3} (x) d x$
81345	Find dy/dx	-y=-3x+xy	$- y = - 3 x + x y$
81346	Find dy/dx	tan(x^2y^4)=3x+y^2	$\tan (x^{2} y^{4}) = 3 x + y^{2}$
81347	Find the Derivative - d/dx	y=((x^6+4)(bx-4))/(x^5)	$y = \frac{(x^{6} + 4) (b x - 4)}{x^{5}}$
81348	Evaluate the Integral	integral from 0 to x^3 of f(t) with respect to t=x^4	$\int_{0}^{x^{3}} f (t) d t = x^{4}$
81349	Evaluate the Limit	limit as x approaches 2 of (x^2-2x)/(x^2+x-6)	$lim_{x \to 2} \frac{x^{2} - 2 x}{x^{2} + x - 6}$
81350	Evaluate the Integral	integral of (3x^2-3x+6)/(4x^3-6x^2+24x) with respect to x	$\int \frac{3 x^{2} - 3 x + 6}{4 x^{3} - 6 x^{2} + 24 x} d x$
81351	Find the Absolute Max and Min over the Interval	f(x)=2/(x^4-16) on interval (0,2)	$f (x) = \frac{2}{x^{4} - 16}$ on interval $(0, 2)$
81352	Evaluate the Integral	integral of csch(1/2x)coth(1/2x) with respect to x	$\int csch (\frac{1}{2} x) \coth (\frac{1}{2} x) d x$
81353	Evaluate the Integral	integral of 1/(x cube root of natural log of x) with respect to x	$\int \frac{1}{x \sqrt[3]{\ln (x)}} d x$
81354	Find the Center and Radius	x^2+y^2+9=4x-10y	$x^{2} + y^{2} + 9 = 4 x - 10 y$
81355	Evaluate the Limit	limit as theta approaches pi of (sin(theta))/(tan(theta))	$lim_{θ \to π} \frac{\sin (θ)}{\tan (θ)}$
81356	Find the Derivative - d/dx	(3(x+2))/(2(x+3)^(1/2))	$\frac{3 (x + 2)}{2 {(x + 3)}^{\frac{1}{2}}}$
81357	Find dy/dx	x^2+3-5y=xy	$x^{2} + 3 - 5 y = x y$
81358	Evaluate the Integral	integral from 1 to 4 of (2- square root of t)/(t^2) with respect to t	$\int_{1}^{4} \frac{2 - \sqrt{t}}{t^{2}} d t$
81359	Integrate Using u-Substitution	integral of (sin(x))/(cos(x)^3) with respect to x	$\int \frac{\sin (x)}{\cos^{3} (x)} d x$
81360	Evaluate the Integral	integral from 1 to 2 of (v^4+4v^8)/(v^5) with respect to v	$\int_{1}^{2} \frac{v^{4} + 4 v^{8}}{v^{5}} d v$
81361	Find the Critical Points	f(x) = square root of 3sin(x)+cos(x)	$f (x) = \sqrt{3} \sin (x) + \cos (x)$
81362	Find the Maximum/Minimum Value	f(x)=-x^3+15x^2-75x+125	$f (x) = - x^{3} + 15 x^{2} - 75 x + 125$
81363	Find the Derivative - d/dy	y/(3y^2-x)	$\frac{y}{3 y^{2} - x}$
81364	Find dy/dx	-5+3y^3=5y^2+3y+x^2	$- 5 + 3 y^{3} = 5 y^{2} + 3 y + x^{2}$
81365	Find the Maximum/Minimum Value	f(x)=12 cube root of x	$f (x) = 12 \sqrt[3]{x}$
81366	Integrate Using u-Substitution	integral of xe^(-x^2) with respect to x , u=-x^2	$\int x e^{- x^{2}} d x$ , $u = - x^{2}$
81367	Find the Antiderivative	e^((x+1)/2)	$e^{\frac{x + 1}{2}}$
81368	Evaluate the Limit	limit as x approaches pi/2 of x^3+5x^2-2x-15	$lim_{x \to \frac{π}{2}} x^{3} + 5 x^{2} - 2 x - 15$
81369	Find dx/dy	x^2y^2-2xy+x^2=1	$x^{2} y^{2} - 2 x y + x^{2} = 1$
81370	Evaluate the Integral	integral from 1 to infinity of 5/(x^4) with respect to x	$\int_{1}^{\infty} \frac{5}{x^{4}} d x$
81371	Find the Derivative - d/dx	y=1/(e^(3x))	$y = \frac{1}{e^{3 x}}$
81372	Find the Derivative - d/dx	e^(2x)-x	$e^{2 x} - x$
81373	Evaluate the Integral	integral from 2 to 5 of (3f(x)+2) with respect to x	$\int_{2}^{5} (3 f (x) + 2) d x$
81374	Evaluate the Limit	limit as x approaches 9 of (x+ square root of x-12)/(x-9)	$lim_{x \to 9} \frac{x + \sqrt{x} - 12}{x - 9}$
81375	Find the Derivative - d/dh	V=pir^2h	$V = π r^{2} h$
81376	Find the Antiderivative	2arctan(x)	$2 \arctan (x)$
81377	Evaluate the Limit	limit as x approaches 4 of ((3x-4)/(x^2+3x-1))^(1/3)	$lim_{x \to 4} {(\frac{3 x - 4}{x^{2} + 3 x - 1})}^{\frac{1}{3}}$
81378	Evaluate the Integral	integral of ( natural log of 10x)/(x^5) with respect to x	$\int \frac{\ln (10 x)}{x^{5}} d x$
81379	Evaluate the Limit	limit as x approaches -4 of (\|x+4\|)/(2x+8)	$lim_{x \to - 4} \frac{\| x + 4 \|}{2 x + 8}$
81380	Find dy/dx	x^3y=-5-3x^2	$x^{3} y = - 5 - 3 x^{2}$
81381	Evaluate the Limit	limit as x approaches -2 of cube root of 2x^2+x+2	$lim_{x \to - 2} \sqrt[3]{2 x^{2} + x + 2}$
81382	Find dy/dx	y = square root of (4x^2)/(6+2x)	$y = \sqrt{\frac{4 x^{2}}{6 + 2 x}}$
81383	Find dy/dx	y^3+xy=-5+5x^3	$y^{3} + x y = - 5 + 5 x^{3}$
81384	Find dy/dx	y^2=-x^3+y	$y^{2} = - x^{3} + y$
81385	Find the Concavity	f(x)=1/6x^4+x^3-10x^2	$f (x) = \frac{1}{6} x^{4} + x^{3} - 10 x^{2}$
81386	Evaluate the Integral	integral of cos(x/1)^2-sin(x) with respect to x	$\int \cos^{2} (\frac{x}{1}) - \sin (x) d x$
81387	Find the Derivative - d/dx	(1+x)^3	${(1 + x)}^{3}$
81388	Find the Maximum/Minimum Value	f(x)=3 cube root of -x-2+6	$f (x) = 3 \sqrt[3]{- x - 2} + 6$
81389	Find dy/dx	-xy^3=-y^2-3	$- x y^{3} = - y^{2} - 3$
81390	Evaluate the Limit	limit as x approaches 0 of (x^2+2x)/( square root of x+9-3)	$lim_{x \to 0} \frac{x^{2} + 2 x}{\sqrt{x + 9} - 3}$
81391	Evaluate the Limit	limit as x approaches c of square root of f(x)	$lim_{x \to c} \sqrt{f (x)}$
81392	Find the Integral	(3t-1)^3dt	${(3 t - 1)}^{3} d t$
81393	Evaluate the Integral	integral of (2x^2-5x-2)/((x-2)^2(x-1)) with respect to x	$\int \frac{2 x^{2} - 5 x - 2}{{(x - 2)}^{2} (x - 1)} d x$
81394	Find the Antiderivative	(2x-13)/((x+1)(x-2))	$\frac{2 x - 13}{(x + 1) (x - 2)}$
81395	Find Where Increasing/Decreasing	f(x)=2/5x^5+4x^4+10x^3+49	$f (x) = \frac{2}{5} x^{5} + 4 x^{4} + 10 x^{3} + 49$
81396	Find the Antiderivative	f(x)=xe^x	$f (x) = x e^{x}$
81397	Evaluate the Summation	sum from x=4 to 12 of 1/4*3^(k-1)	$\sum_{x = 4}^{12} \frac{1}{4} \cdot 3^{k - 1}$
81398	Evaluate the Limit	limit as x approaches -4 of ((x+7)^4)/(x+1)	$lim_{x \to - 4} \frac{{(x + 7)}^{4}}{x + 1}$
81399	Integrate Using u-Substitution	integral of (e^(1/x))/(x^2) with respect to x	$\int \frac{e^{\frac{1}{x}}}{x^{2}} d x$
81400	Find the Antiderivative	4x(1+ natural log of x)	$4 x (1 + \ln (x))$