Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
80101	Solve the Differential Equation	(9xe^(2y)-2)dx+(18x^2e^(2y)-4x)dy=0	$(9 x e^{2 y} - 2) d x + (18 x^{2} e^{2 y} - 4 x) d y = 0$
80102	Solve the Differential Equation	(dy)/(e^(2y))=e^(3x)dx	$\frac{d y}{e^{2 y}} = e^{3 x} d x$
80103	Solve the Differential Equation	(8+x)y''''=5y	$(8 + x) y'' = 5 y$
80104	Solve the Differential Equation	(sin(y)-ysin(x))dx+(cos(x)+xcos(y)-y)dy=0	$(\sin (y) - y \sin (x)) d x + (\cos (x) + x \cos (y) - y) d y = 0$
80105	Solve the Differential Equation	(dy)/(dx)=(9+x)(8+y)	$\frac{d y}{d x} = (9 + x) (8 + y)$
80106	Solve the Differential Equation	(dx)/(dy)+x/y=3/(xy)	$\frac{d x}{d y} + \frac{x}{y} = \frac{3}{x y}$
80107	Find the Derivative - d/dX	1/(X^3)	$\frac{1}{X^{3}}$
80108	Find the Antiderivative	f(x)=2x^(2/3)-5x^3	$f (x) = 2 x^{\frac{2}{3}} - 5 x^{3}$
80109	Evaluate the Limit	limit as x approaches 3 from the right of (x-3)/(\|x^3-3x^2\|)	$lim_{x \to 3^{+}} \frac{x - 3}{\| x^{3} - 3 x^{2} \|}$
80110	Find the Maximum/Minimum Value	y=x^3+3x^2+1	$y = x^{3} + 3 x^{2} + 1$
80111	Find the Derivative - d/dx	y = square root of x+x^(3/2)-8x	$y = \sqrt{x} + x^{\frac{3}{2}} - 8 x$
80112	Find the Derivative - d/dx	y=x^3-2x^2-6x+pi	$y = x^{3} - 2 x^{2} - 6 x + π$
80113	Find the Antiderivative	f(x)=(x^3)/2-3x^-2-2x^3-x^(3/2)	$f (x) = \frac{x^{3}}{2} - 3 x^{- 2} - 2 x^{3} - x^{\frac{3}{2}}$
80114	Evaluate the Limit	limit as x approaches 3 from the left of (x-3)/(\|x^3-3x^2\|)	$lim_{x \to 3^{-}} \frac{x - 3}{\| x^{3} - 3 x^{2} \|}$
80115	Find the Antiderivative	f(x)=x/2-4x^3-x^4	$f (x) = \frac{x}{2} - 4 x^{3} - x^{4}$
80116	Find the Derivative - d/dx	y=1/( cube root of x-1)	$y = \frac{1}{\sqrt[3]{x - 1}}$
80117	Find the Antiderivative	f(x)=-3x^-4+10x^(2/3)-7x	$f (x) = - 3 x^{- 4} + 10 x^{\frac{2}{3}} - 7 x$
80118	Find the Antiderivative	f(x)=3x+8x^3+x^-3+5x^2	$f (x) = 3 x + 8 x^{3} + x^{- 3} + 5 x^{2}$
80119	Evaluate the Limit	limit as x approaches infinity of (2x+3)/(5x^2+4)	$lim_{x \to \infty} \frac{2 x + 3}{5 x^{2} + 4}$
80120	Find the Derivative - d/dx	y=sin(4x)-8x^2+9x+pi	$y = \sin (4 x) - 8 x^{2} + 9 x + π$
80121	Evaluate the Limit	limit as x approaches pi/4 of (tan(x))/x	$lim_{x \to \frac{π}{4}} \frac{\tan (x)}{x}$
80122	Evaluate the Integral	integral of (x+1)(x+a) with respect to x	$\int (x + 1) (x + a) d x$
80123	Evaluate the Integral	integral of (x-1)(x+a) with respect to x	$\int (x - 1) (x + a) d x$
80124	Find the Derivative - d/dx	y=x+3 natural log of 5x-4x^2+e^(2x)-pi	$y = x + 3 \ln (5 x) - 4 x^{2} + e^{2 x} - π$
80125	Evaluate the Limit	limit as x approaches infinity of ( square root of 25x^2-7)/(x+2)	$lim_{x \to \infty} \frac{\sqrt{25 x^{2} - 7}}{x + 2}$
80126	Find the Concavity	x^4-8x^3+18x^2	$x^{4} - 8 x^{3} + 18 x^{2}$
80127	Find the Derivative of the Integral	F(x) = integral from 1 to x^2+1 of (2t+2)/( square root of t+1) with respect to t	$F (x) = \int_{1}^{x^{2} + 1} \frac{2 t + 2}{\sqrt{t + 1}} d t$
80128	Find the Antiderivative	f(x)=8x^4+(x^-2)/2	$f (x) = 8 x^{4} + \frac{x^{- 2}}{2}$
80129	Evaluate the Integral	integral of 2(2^(2x)) with respect to x	$\int 2 (2^{2 x}) d x$
80130	Find the Antiderivative	f(x)=9x^(4/5)+x-2/(x^3)- square root of x	$f (x) = 9 x^{\frac{4}{5}} + x - \frac{2}{x^{3}} - \sqrt{x}$
80131	Find Where Increasing/Decreasing	x^4-8x^3+18x^2	$x^{4} - 8 x^{3} + 18 x^{2}$
80132	Find the Antiderivative	f(x)=1/2x^7	$f (x) = \frac{1}{2} x^{7}$
80133	Evaluate the Limit	limit as w approaches 5 of (2w^4-9w^3+19)^(-1/2)	$lim_{w \to 5} {(2 w^{4} - 9 w^{3} + 19)}^{- \frac{1}{2}}$
80134	Evaluate the Integral	integral from 1 to 2 of (3x^2+4x^3) with respect to x	$\int_{1}^{2} (3 x^{2} + 4 x^{3}) d x$
80135	Solve the Differential Equation	xy'=x^2sin(x)+y	$x y' = x^{2} \sin (x) + y$
80136	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 25x^2-7)/(x+2)	$lim_{x \to - \infty} \frac{\sqrt{25 x^{2} - 7}}{x + 2}$
80137	Find the Antiderivative	x^2+2/(x^2)	$x^{2} + \frac{2}{x^{2}}$
80138	Find the Antiderivative	f(x)=2x-3x^2	$f (x) = 2 x - 3 x^{2}$
80139	Find the Integral	x(x^2+9)^(1/2)	$x {(x^{2} + 9)}^{\frac{1}{2}}$
80140	Evaluate the Integral	integral of (5^(5x+1)-15x^4) with respect to x	$\int (5^{5 x + 1} - 15 x^{4}) d x$
80141	Evaluate the Limit	limit as x approaches infinity of (x^3+5)/(x(2x^2+3))	$lim_{x \to \infty} \frac{x^{3} + 5}{x (2 x^{2} + 3)}$
80142	Find the Antiderivative	square root of x-2/( square root of x)	$\sqrt{x} - \frac{2}{\sqrt{x}}$
80143	Evaluate the Integral	integral from 0 to a of 3x^2 with respect to x=1	$\int_{0}^{a} 3 x^{2} d x = 1$
80144	Evaluate the Limit	limit as x approaches 1 of (e^x-e)/(x-1)	$lim_{x \to 1} \frac{e^{x} - e}{x - 1}$
80145	Evaluate the Integral	integral of (-2x^-3+20x^-5) with respect to x	$\int (- 2 x^{- 3} + 20 x^{- 5}) d x$
80146	Evaluate the Integral	integral of 2(2^x) with respect to x	$\int 2 (2^{x}) d x$
80147	Find the Derivative - d/dx	y=((3x-1)/(x^2+3))^2	$y = {(\frac{3 x - 1}{x^{2} + 3})}^{2}$
80148	Evaluate the Limit	limit as x approaches infinity of (e^x)/(x+1)	$lim_{x \to \infty} \frac{e^{x}}{x + 1}$
80149	Find the Derivative - d/dx	x+ square root of x+1	$x + \sqrt{x + 1}$
80150	Evaluate the Limit	limit as x approaches 1 of (4- square root of x+15)/(1-x^2)	$lim_{x \to 1} \frac{4 - \sqrt{x + 15}}{1 - x^{2}}$
80151	Evaluate the Integral	integral from 0 to a of 6x^2 with respect to x=-2	$\int_{0}^{a} 6 x^{2} d x = - 2$
80152	Evaluate the Limit	limit as x approaches infinity of (-x^2-x)/(4x^2+1)	$lim_{x \to \infty} \frac{- x^{2} - x}{4 x^{2} + 1}$
80153	Evaluate the Integral	integral of (7x^3)^2 with respect to x	$\int {(7 x^{3})}^{2} d x$
80154	Find the Antiderivative	f(x)=1/(2x^3)	$f (x) = \frac{1}{2 x^{3}}$
80155	Find the Derivative - d/dx	y=3^(x natural log of x)	$y = 3^{x \ln (x)}$
80156	Evaluate the Limit	limit as x approaches infinity of (3/5)^(1/x)	$lim_{x \to \infty} {(\frac{3}{5})}^{\frac{1}{x}}$
80157	Find the Antiderivative	f(x)=2x+4x^3+ square root of x^3+8	$f (x) = 2 x + 4 x^{3} + \sqrt{x^{3}} + 8$
80158	Find the Derivative - d/dx	y=tan(x)+7x^2-pix+2	$y = \tan (x) + 7 x^{2} - π x + 2$
80159	Find the Antiderivative	f(x)=12x^3+24/(x^4)-2/( square root of x)	$f (x) = 12 x^{3} + \frac{24}{x^{4}} - \frac{2}{\sqrt{x}}$
80160	Evaluate the Integral	integral from negative infinity to 0 of (xe^x)/((x+1)^2) with respect to x	$\int_{- \infty}^{0} \frac{x e^{x}}{{(x + 1)}^{2}} d x$
80161	Evaluate the Integral	integral of (6^(3x^2-3x))(6x-3) with respect to x	$\int (6^{3 x^{2} - 3 x}) (6 x - 3) d x$
80162	Evaluate the Limit	limit as x approaches 5 of (x^2-5x)/( square root of x+4-3)	$lim_{x \to 5} \frac{x^{2} - 5 x}{\sqrt{x + 4} - 3}$
80163	Find the Derivative - d/dx	y=arctan(4x^2-3)	$y = \arctan (4 x^{2} - 3)$
80164	Find the Antiderivative	f(x)=1/x-3/(x^3)	$f (x) = \frac{1}{x} - \frac{3}{x^{3}}$
80165	Find the Fourth Derivative	f(x)=x^5-2/(x^3)-4x+2	$f (x) = x^{5} - \frac{2}{x^{3}} - 4 x + 2$
80166	Evaluate the Limit	limit as x approaches 5 of (x^2-25)/(x-5)+ square root of x^2+7	$lim_{x \to 5} \frac{x^{2} - 25}{x - 5} + \sqrt{x^{2} + 7}$
80167	Find the Antiderivative	(x^2+1)^2	${(x^{2} + 1)}^{2}$
80168	Evaluate the Limit	limit as x approaches infinity of ( square root of x^2)/x	$lim_{x \to \infty} \frac{\sqrt{x^{2}}}{x}$
80169	Evaluate the Limit	limit as x approaches -1 of (x^2+x)/(x^3+1)	$lim_{x \to - 1} \frac{x^{2} + x}{x^{3} + 1}$
80170	Find dy/dx	2x^2+y^2-xy=4	$2 x^{2} + y^{2} - x y = 4$
80171	Find the Antiderivative	f(x)=(x^2)/4+2/(3x^2)- square root of x+pi	$f (x) = \frac{x^{2}}{4} + \frac{2}{3 x^{2}} - \sqrt{x} + π$
80172	Evaluate the Limit	limit as x approaches 0 of (2/( square root of x+4)-1/( square root of x+1))/(x square root of x+3)	$lim_{x \to 0} \frac{\frac{2}{\sqrt{x + 4}} - \frac{1}{\sqrt{x + 1}}}{x \sqrt{x + 3}}$
80173	Find the Antiderivative	(x^2)/(x+1)	$\frac{x^{2}}{x + 1}$
80174	Find dy/dx	x^2y-x/y=-2	$x^{2} y - \frac{x}{y} = - 2$
80175	Find the Antiderivative	f(x)=2x^3-4x^2+2x	$f (x) = 2 x^{3} - 4 x^{2} + 2 x$
80176	Find the Derivative Using Chain Rule - d/dx	fx=sin(e^(2x)+6x^2)	$f x = \sin (e^{2 x} + 6 x^{2})$
80177	Find the Derivative - d/dx	y=1/(sin(20x))	$y = \frac{1}{\sin (20 x)}$
80178	Find the Derivative - d/dx	y = fourth root of 8x^2	$y = \sqrt[4]{8 x^{2}}$
80179	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (cos(6x)-cos(7x))/(x^2)	$lim_{x \to 0} \frac{\cos (6 x) - \cos (7 x)}{x^{2}}$
80180	Evaluate the Limit	limit as x approaches infinity of ((x-4)/(x+3))^(2x+1)	$lim_{x \to \infty} {(\frac{x - 4}{x + 3})}^{2 x + 1}$
80181	Find the Antiderivative	x^2*e^x	$x^{2} \cdot e^{x}$
80182	Find the Tangent Line at x=1	f(x)=x^3-6x^2+1 is concave down at x=1	$f (x) = x^{3} - 6 x^{2} + 1$ is concave down at $x = 1$
80183	Find dx/dy	y=(4x^2-16)/(x-2)	$y = \frac{4 x^{2} - 16}{x - 2}$
80184	Find the Antiderivative	e^x-e^(-x)	$e^{x} - e^{- x}$
80185	Evaluate the Limit	limit as x approaches 1 of (x^2-x^-2)/(x-x^-1)	$lim_{x \to 1} \frac{x^{2} - x^{- 2}}{x - x^{- 1}}$
80186	Evaluate the Integral	integral of (x^3-3x+e^(3x)) with respect to x	$\int (x^{3} - 3 x + e^{3 x}) d x$
80187	Find the Derivative - d/dv	v=1/3pir^2h	$v = \frac{1}{3} π r^{2} h$
80188	Evaluate the Limit	limit as x approaches 1 of (e^(x-1)-1)/(x-1)	$lim_{x \to 1} \frac{e^{x - 1} - 1}{x - 1}$
80189	Find the Third Derivative	7^x+1102	$7^{x} + 1102$
80190	Find the Antiderivative	(x-1)/(x^2)	$\frac{x - 1}{x^{2}}$
80191	Find the Antiderivative	1/x-3/(x^3)	$\frac{1}{x} - \frac{3}{x^{3}}$
80192	Find the Antiderivative	x*e^(2x)	$x \cdot e^{2 x}$
80193	Evaluate the Integral	integral of (2^x+2) with respect to x	$\int (2^{x} + 2) d x$
80194	Find the Antiderivative	natural log of x+1	$\ln (x + 1)$
80195	Find the Antiderivative	1/(x^2-3x+2)	$\frac{1}{x^{2} - 3 x + 2}$
80196	Evaluate the Integral	integral of x(2x^2+1) with respect to x	$\int x (2 x^{2} + 1) d x$
80197	Evaluate the Integral	integral of (cot(x)^2+1) with respect to x	$\int (\cot^{2} (x) + 1) d x$
80198	Integrate By Parts	integral of x/(e^(2x)) with respect to x	$\int \frac{x}{e^{2 x}} d x$
80199	Evaluate the Integral	integral of (5x^4+5x)/x with respect to x	$\int \frac{5 x^{4} + 5 x}{x} d x$
80200	Find Where Increasing/Decreasing	f(x) = cube root of x-1	$f (x) = \sqrt[3]{x - 1}$