Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
81101	Integrate Using u-Substitution	integral of x^2-x+x^-1 with respect to x	$\int x^{2} - x + x^{- 1} d x$
81102	Find the Critical Points	f(x)=x^3-3/2x^2-36x	$f (x) = x^{3} - \frac{3}{2} x^{2} - 36 x$
81103	Evaluate Using L'Hospital's Rule	L = limit as x approaches c of (f(x))/(g(x))	$L = lim_{x \to c} \frac{f (x)}{g (x)}$
81104	Evaluate the Limit	limit as x approaches 0 of (1-cos(x)+sin(3x))/(1-cos(x)+tan(2x))	$lim_{x \to 0} \frac{1 - \cos (x) + \sin (3 x)}{1 - \cos (x) + \tan (2 x)}$
81105	Find the Antiderivative	1/(cos(x)^4)	$\frac{1}{\cos^{4} (x)}$
81106	Evaluate the Integral	integral of (x^8+x^6-x^2) with respect to x	$\int (x^{8} + x^{6} - x^{2}) d x$
81107	Evaluate the Integral	integral from 1/2 to 3 of (2-1/x) with respect to x	$\int_{\frac{1}{2}}^{3} (2 - \frac{1}{x}) d x$
81108	Find the Derivative - d/dX	X^2+2x+1	$X^{2} + 2 x + 1$
81109	Find the Antiderivative	f(x)=e^x+1/x	$f (x) = e^{x} + \frac{1}{x}$
81110	Find the Derivative - d/dx	xarctanh(x)+ natural log of square root of 1-x^2	$x arctanh (x) + \ln (\sqrt{1 - x^{2}})$
81111	Find the Center and Radius	x^2+y^2+20x+100=0	$x^{2} + y^{2} + 20 x + 100 = 0$
81112	Find the Antiderivative	e^(2x)-e^x	$e^{2 x} - e^{x}$
81113	Evaluate the Limit	limit as x approaches -6 of ((x+2)/(x^2-12)-1/x)/(x+6)	$lim_{x \to - 6} \frac{\frac{x + 2}{x^{2} - 12} - \frac{1}{x}}{x + 6}$
81114	Find the Derivative - d/dx	1/(x^2)dx	$\frac{1}{x^{2}} d x$
81115	Find the Antiderivative	f(x)=1/(5x-2)	$f (x) = \frac{1}{5 x - 2}$
81116	Find the Local Maxima and Minima	f(x)=-1/5x^5-2x^4-5x^3+9	$f (x) = - \frac{1}{5} x^{5} - 2 x^{4} - 5 x^{3} + 9$
81117	Find the Derivative - d/dx	square root of x+x^(3/2)-8x	$\sqrt{x} + x^{\frac{3}{2}} - 8 x$
81118	Find the Derivative - d/dx	(5-2x)e^x	$(5 - 2 x) e^{x}$
81119	Find dz/dx	z=y(3+2x)^4	$z = y {(3 + 2 x)}^{4}$
81120	Evaluate the Integral	integral of (e^(3x)-18e^(-4x)) with respect to x	$\int (e^{3 x} - 18 e^{- 4 x}) d x$
81121	Find the Inflection Points	f(x)=-1/2x^4+42x^2	$f (x) = - \frac{1}{2} x^{4} + 42 x^{2}$
81122	Evaluate the Limit	limit as x approaches 0 of tan(pi/4)	$lim_{x \to 0} \tan (\frac{π}{4})$
81123	Integrate Using u-Substitution	integral from 1 to 2 of (e^(1/(x^4)))/(x^5) with respect to x	$\int_{1}^{2} \frac{e^{\frac{1}{x^{4}}}}{x^{5}} d x$
81124	Find the Antiderivative	f(x)=3/( square root of 2x-6)-2/(x^3)	$f (x) = \frac{3}{\sqrt{2 x - 6}} - \frac{2}{x^{3}}$
81125	Find the Antiderivative	4x*e^(2x)	$4 x \cdot e^{2 x}$
81126	Find the Antiderivative	e^x-1	$e^{x} - 1$
81127	Find the Inflection Points	-1/10x^5-2x^4-12x^3	$- \frac{1}{10} x^{5} - 2 x^{4} - 12 x^{3}$
81128	Evaluate the Limit	limit as x approaches infinity of 4-3x-x^3	$lim_{x \to \infty} 4 - 3 x - x^{3}$
81129	Find the Inflection Points	f(x)=2/15x^6-x^5-8x^4	$f (x) = \frac{2}{15} x^{6} - x^{5} - 8 x^{4}$
81130	Find dy/dx	x^4+x^2y^2-xy^3=20	$x^{4} + x^{2} y^{2} - x y^{3} = 20$
81131	Evaluate the Limit	limit as x approaches 0 of (x^2-x-2)/(x^3-6x^2-7x+1)	$lim_{x \to 0} \frac{x^{2} - x - 2}{x^{3} - 6 x^{2} - 7 x + 1}$
81132	Find the Derivative - d/dx	(e^x)/(1+e^(2x))	$\frac{e^{x}}{1 + e^{2 x}}$
81133	Find the Center and Radius	x^2+8y^2+4x-y+20=0	$x^{2} + 8 y^{2} + 4 x - y + 20 = 0$
81134	Evaluate the Limit	limit as x approaches infinity of (6-4x^2+x^3)/(4+5x-7x^2)	$lim_{x \to \infty} \frac{6 - 4 x^{2} + x^{3}}{4 + 5 x - 7 x^{2}}$
81135	Find the Second Derivative	S(t)=1/3t^3-3.5t^2+10t	$S (t) = \frac{1}{3} t^{3} - 3.5 t^{2} + 10 t$
81136	Find the Integral	(e^x)/(1+e^x)	$\frac{e^{x}}{1 + e^{x}}$
81137	Find the Derivative - d/dx	(x^2-5/4)e^x	$(x^{2} - \frac{5}{4}) e^{x}$
81138	Find the Antiderivative	f(x)=x square root of x-4/( square root of x)	$f (x) = x \sqrt{x} - \frac{4}{\sqrt{x}}$
81139	Find dy/dx	-xy^3+5y=3-x^3	$- x y^{3} + 5 y = 3 - x^{3}$
81140	Evaluate the Integral	integral of (7(4-x^2))/((x-4)(x-2)(x+3)) with respect to x	$\int \frac{7 (4 - x^{2})}{(x - 4) (x - 2) (x + 3)} d x$
81141	Find dy/dx	-xy^3-x=4y^3+4	$- x y^{3} - x = 4 y^{3} + 4$
81142	Find the Derivative - d/dx	6e^(4x)-2e^(3x)-4	$6 e^{4 x} - 2 e^{3 x} - 4$
81143	Find the Antiderivative	x/x	$\frac{x}{x}$
81144	Find the Antiderivative	f(x) = square root of x+2x^2 square root of x	$f (x) = \sqrt{x} + 2 x^{2} \sqrt{x}$
81145	Evaluate the Integral	integral from square root of pi/2 to square root of pi of 9theta^3cos(theta^2) with respect to theta	$\int_{\sqrt{\frac{π}{2}}}^{\sqrt{π}} 9 θ^{3} \cos (θ^{2}) d θ$
81146	Find the Antiderivative	f(x)=(2-3x)^2	$f (x) = {(2 - 3 x)}^{2}$
81147	Integrate Using u-Substitution	integral of (x^3)/( square root of 1-x^2) with respect to x	$\int \frac{x^{3}}{\sqrt{1 - x^{2}}} d x$
81148	Find the Percentage Rate of Change	f(t)=1/3(1.26)^t	$f (t) = \frac{1}{3} {(1.26)}^{t}$
81149	Find Where Increasing/Decreasing	(x^2)/((x-2)^3)	$\frac{x^{2}}{{(x - 2)}^{3}}$
81150	Find dx/dy	y=1/( cube root of x-1)	$y = \frac{1}{\sqrt[3]{x - 1}}$
81151	Find the Maximum/Minimum Value	y=x^3-4x	$y = x^{3} - 4 x$
81152	Solve the Differential Equation	y'-2y=0	$y' - 2 y = 0$
81153	Find the Antiderivative	(x+3)/(x^2+3x+2)	$\frac{x + 3}{x^{2} + 3 x + 2}$
81154	Find the Third Derivative	f(x)=x^4-6	$f (x) = x^{4} - 6$
81155	Find the Third Derivative	5x^4-4x^3+2	$5 x^{4} - 4 x^{3} + 2$
81156	Evaluate the Integral	If integral from 0 to a of 6x^2 with respect to x=-2	If $\int_{0}^{a} 6 x^{2} d x = - 2$
81157	Find the Antiderivative	f(x)=1/( square root of 7x-9)	$f (x) = \frac{1}{\sqrt{7 x - 9}}$
81158	Evaluate the Limit	limit as x approaches 0 from the right of sinh(3x)^x	$lim_{x \to 0^{+}} {\sinh (3 x)}^{x}$
81159	Find the Derivative - d/dx	-15/(16(x+1)^(7/2))	$- \frac{15}{16 {(x + 1)}^{\frac{7}{2}}}$
81160	Evaluate the Integral	integral from 0 to 1 of (1-8v^3+16v^7) with respect to v	$\int_{0}^{1} (1 - 8 v^{3} + 16 v^{7}) d v$
81161	Find the Antiderivative	3/( cube root of x+3)	$\frac{3}{\sqrt[3]{x + 3}}$
81162	Find the Derivative - d/dx	\|2x-1\|	$\| 2 x - 1 \|$
81163	Find dy/dx	y+x^3y-5x=0	$y + x^{3} y - 5 x = 0$
81164	Find the Maximum/Minimum Value	x^4-x^5	$x^{4} - x^{5}$
81165	Evaluate the Integral	integral from -3 to k of x^2 with respect to x=0	$\int_{- 3}^{k} x^{2} d x = 0$
81166	Evaluate the Integral	integral of -1/(4x square root of 4-(2x)^2) with respect to x	$\int \frac{- 1}{4 x \sqrt{4 - {(2 x)}^{2}}} d x$
81167	Find dy/dx	3xy-x^3=5	$3 x y - x^{3} = 5$
81168	Find the Maximum/Minimum Value	f(x)=e^(x^2-1)	$f (x) = e^{x^{2} - 1}$
81169	Find the Maximum/Minimum Value	h(x)=x^3e^(-x)	$h (x) = x^{3} e^{- x}$
81170	Find the Concavity	f(x)=-1/3x^3-7x^2	$f (x) = - \frac{1}{3} x^{3} - 7 x^{2}$
81171	Find the Concavity	x^5+5x^4	$x^{5} + 5 x^{4}$
81172	Find the Inflection Points	f(x)=-1/6x^4+x^2	$f (x) = - \frac{1}{6} x^{4} + x^{2}$
81173	Evaluate the Limit	limit as x approaches 0 of ((3+x)^4-81)/(6x)	$lim_{x \to 0} \frac{{(3 + x)}^{4} - 81}{6 x}$
81174	Evaluate the Integral	integral from 0 to 1 of 5^((3x)/2) with respect to x	$\int_{0}^{1} 5^{\frac{3 x}{2}} d x$
81175	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ((3x)/(3x+1))^x	$lim_{x \to \infty} {(\frac{3 x}{3 x + 1})}^{x}$
81176	Evaluate the Integral	integral of (x^(3/4)-1/(x^(3/4))) with respect to x	$\int (x^{\frac{3}{4}} - \frac{1}{x^{\frac{3}{4}}}) d x$
81177	Evaluate the Limit	limit as x approaches 4 of (x^3 square root of x-128)/(x-4)	$lim_{x \to 4} \frac{x^{3} \sqrt{x} - 128}{x - 4}$
81178	Find the Derivative - d/dx	y=((3x^2+2)/(x+1))^7	$y = {(\frac{3 x^{2} + 2}{x + 1})}^{7}$
81179	Find the Derivative - d/dx	natural log of ((x+1)/(2x-1))^2	$\ln ({(\frac{x + 1}{2 x - 1})}^{2})$
81180	Find the Antiderivative	x/(x^2)	$\frac{x}{x^{2}}$
81181	Evaluate the Limit	limit as x approaches 0 of (x/(x+1))^x	$lim_{x \to 0} {(\frac{x}{x + 1})}^{x}$
81182	Find the Integral	natural log of x+1	$\ln (x + 1)$
81183	Evaluate the Limit	limit as x approaches 0 of (x+1)^(cot(x))	$lim_{x \to 0} {(x + 1)}^{\cot (x)}$
81184	Find the Maximum/Minimum Value	y=cos(x+pi/4)	$y = \cos (x + \frac{π}{4})$
81185	Find the Antiderivative	square root of 1-x	$\sqrt{1 - x}$
81186	Evaluate the Integral	integral of 2/( cube root of 3x) with respect to x	$\int \frac{2}{\sqrt[3]{3 x}} d x$
81187	Evaluate the Integral	integral of (7 square root of x^3+6 cube root of x^2) with respect to x	$\int (7 \sqrt{x^{3}} + 6 \sqrt[3]{x^{2}}) d x$
81188	Find the Antiderivative	1/(x(x-1))	$\frac{1}{x (x - 1)}$
81189	Evaluate the Limit	limit as x approaches pi/2 of 1/(cos(x))-tan(x)	$lim_{x \to \frac{π}{2}} \frac{1}{\cos (x)} - \tan (x)$
81190	Evaluate the Limit	limit as x approaches infinity of ( square root of x^2+3)/(2x+1)	$lim_{x \to \infty} \frac{\sqrt{x^{2} + 3}}{2 x + 1}$
81191	Evaluate the Limit	limit as x approaches -1 of (4x^3+9x^2-3x-8)/(2x^2-5x+1)	$lim_{x \to - 1} \frac{4 x^{3} + 9 x^{2} - 3 x - 8}{2 x^{2} - 5 x + 1}$
81192	Find the Center and Radius	2x^2+2y^2-8=0	$2 x^{2} + 2 y^{2} - 8 = 0$
81193	Find the Derivative - d/dx	(x^2+1)^(3/2)	${(x^{2} + 1)}^{\frac{3}{2}}$
81194	Evaluate the Limit	limit as x approaches 1/2 of (2x^2+7x-4)/(2x-1)	$lim_{x \to \frac{1}{2}} \frac{2 x^{2} + 7 x - 4}{2 x - 1}$
81195	Find the Derivative - d/dx	y=2/3x^4+5x-x^-3	$y = \frac{2}{3} x^{4} + 5 x - x^{- 3}$
81196	Find the Antiderivative	(1/x)^2	${(\frac{1}{x})}^{2}$
81197	Evaluate the Integral	integral of x(3x+5)(4x-5) with respect to x	$\int x (3 x + 5) (4 x - 5) d x$
81198	Find the Upper and Lower Bounds	f(x)=x^4-x^3-2x^2+5x-6	$f (x) = x^{4} - x^{3} - 2 x^{2} + 5 x - 6$
81199	Find Where Increasing/Decreasing	f(x)=-2/3x	$f (x) = - \frac{2}{3} x$
81200	Evaluate the Integral	integral from 0 to pi/3 of (3sin(theta)+3sin(theta)tan(theta)^2)/(sec(theta)^2) with respect to theta	$\int_{0}^{\frac{π}{3}} \frac{3 \sin (θ) + 3 \sin (θ) \tan^{2} (θ)}{\sec^{2} (θ)} d θ$