Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
81901	Find the Antiderivative	square root of x+ cube root of x+ fourth root of x	$\sqrt{x} + \sqrt[3]{x} + \sqrt[4]{x}$
81902	Find the Antiderivative	2x^3-2/3x^2+5x	$2 x^{3} - \frac{2}{3} x^{2} + 5 x$
81903	Find the Maximum/Minimum Value	f(x)=0.5x^3-2x+2.5	$f (x) = 0.5 x^{3} - 2 x + 2.5$
81904	Find dy/dx	-y^3+5y^2=4x^2	$- y^{3} + 5 y^{2} = 4 x^{2}$
81905	Find the Derivative - d/dA	sin(A)^2	$\sin^{2} (A)$
81906	Find dy/dx	y=tan(x)+7x^2-pix+2	$y = \tan (x) + 7 x^{2} - π x + 2$
81907	Evaluate the Integral	integral from 0 to pi/4 of sec(theta)^4tan(theta)^4 with respect to theta	$\int_{0}^{\frac{π}{4}} \sec^{4} (θ) \tan^{4} (θ) d θ$
81908	Find the Derivative - d/dx	sec(x)-1	$\sec (x) - 1$
81909	Evaluate the Integral	integral of 6(3x+1)e^(15x^2+10x-15) with respect to x	$\int 6 (3 x + 1) e^{15 x^{2} + 10 x - 15} d x$
81910	Find dy/dx	(x+2y)^6=y^2	${(x + 2 y)}^{6} = y^{2}$
81911	Evaluate the Integral	integral from 0 to pi/4 of 4sec(theta)^4tan(theta)^4 with respect to theta	$\int_{0}^{\frac{π}{4}} 4 \sec^{4} (θ) \tan^{4} (θ) d θ$
81912	Integrate Using u-Substitution	integral of sin(theta)^2cos(theta) with respect to theta , u=sin(theta)	$\int \sin^{2} (θ) \cos (θ) d θ$ , $u = \sin (θ)$
81913	Find the Antiderivative	xe^xdx	$x e^{x} d x$
81914	Evaluate the Limit	limit as h approaches 0 of (-9 square root of h+4+18)/h	$lim_{h \to 0} \frac{- 9 \sqrt{h + 4} + 18}{h}$
81915	Find the Derivative - d/dO	OH	$O H$
81916	Find the Concavity	f(x)=-3/5x^5+7x^4	$f (x) = - \frac{3}{5} x^{5} + 7 x^{4}$
81917	Find the Derivative - d/dx	1/x+x	$\frac{1}{x} + x$
81918	Find the Antiderivative	x^2e^(2x)	$x^{2} e^{2 x}$
81919	Evaluate the Limit	limit as x approaches 2 of (3x^2-6x)/(6x^2+2x)	$lim_{x \to 2} \frac{3 x^{2} - 6 x}{6 x^{2} + 2 x}$
81920	Integrate Using u-Substitution	integral from 0 to pi/6 of (sin(t))/(cos(t)^2) with respect to t	$\int_{0}^{\frac{π}{6}} \frac{\sin (t)}{\cos^{2} (t)} d t$
81921	Evaluate the Integral	integral from 0 to 1 of (x^11+11^x) with respect to x	$\int_{0}^{1} (x^{11} + 11^{x}) d x$
81922	Evaluate the Integral	integral of (5x^-3-x) with respect to x	$\int (5 x^{- 3} - x) d x$
81923	Find the Antiderivative	(2x+3)/(2-x)	$\frac{2 x + 3}{2 - x}$
81924	Evaluate the Limit	limit as x approaches 3 of ( square root of 12-x)/(x+3)	$lim_{x \to 3} \frac{\sqrt{12 - x}}{x + 3}$
81925	Evaluate the Limit	limit as x approaches 0 of f(x-1)g(x)	$lim_{x \to 0} f (x - 1) g (x)$
81926	Find the Antiderivative	(x^2)/(1+x)	$\frac{x^{2}}{1 + x}$
81927	Integrate Using u-Substitution	integral from 1 to 2 of (e^(1/(x^3)))/(x^4) with respect to x	$\int_{1}^{2} \frac{e^{\frac{1}{x^{3}}}}{x^{4}} d x$
81928	Find dy/dx	2x^3+4-x^2+y^2-x=0	$2 x^{3} + 4 - x^{2} + y^{2} - x = 0$
81929	Find the Antiderivative	x natural log of x+2	$x \ln (x + 2)$
81930	Find dy/dx	-y=-2x^2+3xy^3	$- y = - 2 x^{2} + 3 x y^{3}$
81931	Find Where Increasing/Decreasing	f(x)=-2(1/2)^x+1	$f (x) = - 2 {(\frac{1}{2})}^{x} + 1$
81932	Evaluate the Limit	limit as x approaches 5 of (x^4-5x^3)/(25-x^2)	$lim_{x \to 5} \frac{x^{4} - 5 x^{3}}{25 - x^{2}}$
81933	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ((x-4)/(x+3))^(2x+1)	$lim_{x \to \infty} {(\frac{x - 4}{x + 3})}^{2 x + 1}$
81934	Find dy/dx	-x^3=-4+4y^2-3y^3	$- x^{3} = - 4 + 4 y^{2} - 3 y^{3}$
81935	Find the Second Derivative	x^(2/3)-3	$x^{\frac{2}{3}} - 3$
81936	Find the Derivative - d/dx	5^(3x^2-1)	$5^{3 x^{2} - 1}$
81937	Find the Antiderivative	square root of e^(4x-2)	$\sqrt{e^{4 x - 2}}$
81938	Find the Derivative - d/dx	(( natural log of x)^2)/x	$\frac{\ln^{2} (x)}{x}$
81939	Find the Derivative of the Integral	g(x) = integral from 0 to x of 3t^2+2t with respect to t	$g (x) = \int_{0}^{x} 3 t^{2} + 2 t d t$
81940	Evaluate the Limit	limit as x approaches negative infinity of (4x+8)/(5x)	$lim_{x \to - \infty} \frac{4 x + 8}{5 x}$
81941	Integrate Using u-Substitution	integral of (sin( natural log of x))/x with respect to x	$\int \frac{\sin (\ln (x))}{x} d x$
81942	Find the Absolute Max and Min over the Interval	f(x)=x^4-8x^2+2 on [-3,1]	$f (x) = x^{4} - 8 x^{2} + 2$ on $[- 3, 1]$
81943	Evaluate the Limit	limit as x approaches 3 from the left of (9-x^2)/(4x\|x-3\|)	$lim_{x \to 3^{-}} \frac{9 - x^{2}}{4 x \| x - 3 \|}$
81944	Evaluate the Integral	integral from 0 to pi/2 of (sin(x))/(1+cos(x)^2) with respect to x	$\int_{0}^{\frac{π}{2}} \frac{\sin (x)}{1 + \cos^{2} (x)} d x$
81945	Evaluate the Integral	integral from 2 to infinity of 2e^(-2x-4) with respect to x	$\int_{2}^{\infty} 2 e^{- 2 x - 4} d x$
81946	Find dy/dx	x^2y-2=3y^2	$x^{2} y - 2 = 3 y^{2}$
81947	Evaluate the Limit	limit as x approaches 1 of ( cube root of x+ square root of x-2)/(x-1)	$lim_{x \to 1} \frac{\sqrt[3]{x} + \sqrt{x} - 2}{x - 1}$
81948	Find dy/dx	-4y^2-2x^3=3+xy	$- 4 y^{2} - 2 x^{3} = 3 + x y$
81949	Evaluate the Limit	limit as x approaches 0 of -2e^(-2x^4-1/10)	$lim_{x \to 0} - 2 e^{- 2 x^{4} - \frac{1}{10}}$
81950	Evaluate the Integral	2/pi integral from -1 to 0 of 1/( square root of 1-x^2) with respect to x	$\frac{2}{π} \int_{- 1}^{0} \frac{1}{\sqrt{1 - x^{2}}} d x$
81951	Find the Derivative - d/dx	y = log of 1-4tan(x)	$y = \log (1 - 4 \tan (x))$
81952	Evaluate the Integral	integral of 5u^2(3+2u^3)^(2/3) with respect to u	$\int 5 u^{2} {(3 + 2 u^{3})}^{\frac{2}{3}} d u$
81953	Integrate Using u-Substitution	integral of (e^x)/(1+e^x) with respect to x	$\int \frac{e^{x}}{1 + e^{x}} d x$
81954	Evaluate the Limit	limit as x approaches 0 of (1-cos(x)+sin(x))/(1-cos(x)-sin(x))	$lim_{x \to 0} \frac{1 - \cos (x) + \sin (x)}{1 - \cos (x) - \sin (x)}$
81955	Find the Antiderivative	x^3e^x	$x^{3} e^{x}$
81956	Evaluate Using L'Hospital's Rule	limit as x approaches -2 of (3e^(-2-x)-3)/(2x^2-8)	$lim_{x \to - 2} \frac{3 e^{- 2 - x} - 3}{2 x^{2} - 8}$
81957	Find dy/dx	-3x^3+xy-3=0	$- 3 x^{3} + x y - 3 = 0$
81958	Find the Derivative - d/dx	y=arcsec(3x)+arccsc(3x)	$y = arcsec (3 x) + arccsc (3 x)$
81959	Find the Derivative - d/dx	1/(e^x-1)	$\frac{1}{e^{x} - 1}$
81960	Evaluate the Integral	integral of xf(x) with respect to x	$\int x f (x) d x$
81961	Evaluate the Limit	limit as x approaches infinity of 3+2x-5x^2	$lim_{x \to \infty} 3 + 2 x - 5 x^{2}$
81962	Find the Antiderivative	f(x)=cos(x)^4	$f (x) = \cos^{4} (x)$
81963	Find dy/dx	4x^2y^7-2x=x^5+4y^3	$4 x^{2} y^{7} - 2 x = x^{5} + 4 y^{3}$
81964	Find the Maximum/Minimum Value	f(x)=x^4-3x^2+3x+1	$f (x) = x^{4} - 3 x^{2} + 3 x + 1$
81965	Evaluate the Limit	limit as x approaches -1 of ((x+1)^2(x-1))/(x^3+1)	$lim_{x \to - 1} \frac{{(x + 1)}^{2} (x - 1)}{x^{3} + 1}$
81966	Evaluate the Integral	integral of (2x^2+4x-3)/(x^2) with respect to x	$\int \frac{2 x^{2} + 4 x - 3}{x^{2}} d x$
81967	Find dy/dx	-y^2-xy^3-x^3=-2	$- y^{2} - x y^{3} - x^{3} = - 2$
81968	Evaluate Using Summation Formulas	sum from i=1 to 25 of (i^2+2)^2	$\sum_{i = 1}^{25} {(i^{2} + 2)}^{2}$
81969	Find the Antiderivative	f(x)=x/(x+1)	$f (x) = \frac{x}{x + 1}$
81970	Find the Derivative - d/dx	(x+x^2)e^(-2x)	$(x + x^{2}) e^{- 2 x}$
81971	Find the Concavity	f(x)=(1-2x)^3	$f (x) = {(1 - 2 x)}^{3}$
81972	Find the Antiderivative	f(x)=9/(x^10)+8/(x^9)	$f (x) = \frac{9}{x^{10}} + \frac{8}{x^{9}}$
81973	Evaluate the Limit	limit as x approaches 0 of (x^2-2x+sin(x))/x	$lim_{x \to 0} \frac{x^{2} - 2 x + \sin (x)}{x}$
81974	Find dx/dy	y=sin(2x)	$y = \sin (2 x)$
81975	Find the Derivative - d/dx	y=(5+tan(x))/(2x+e^x)	$y = \frac{5 + \tan (x)}{2 x + e^{x}}$
81976	Evaluate the Limit	limit as x approaches -1 from the left of F(x)	$lim_{x \to {(- 1)}^{-}} F (x)$
81977	Find the Derivative - d/dx	2x-1/x	$2 x - \frac{1}{x}$
81978	Find the Antiderivative	(2x+3)/(x+1)	$\frac{2 x + 3}{x + 1}$
81979	Find dy/dx	2-x^3=-x^2-2y^3	$2 - x^{3} = - x^{2} - 2 y^{3}$
81980	Evaluate the Limit	limit as x approaches 1/(()/())*2 of 2e^(x^4+2/9)	$lim_{x \to \frac{1}{\frac{}{}} \cdot 2} 2 e^{x^{4} + \frac{2}{9}}$
81981	Integrate Using u-Substitution	integral of x^3(2+x^4)^5 with respect to x	$\int x^{3} {(2 + x^{4})}^{5} d x$
81982	Evaluate the Integral	integral of -2(5x^2+2x)e^(3x) with respect to x	$\int - 2 (5 x^{2} + 2 x) e^{3 x} d x$
81983	Find dy/dx	y=x^2-x^2cos(x)	$y = x^{2} - x^{2} \cos (x)$
81984	Integrate Using u-Substitution	integral of square root of 1-x^2 with respect to x	$\int \sqrt{1 - x^{2}} d x$
81985	Find dy/dx	5x^2+y^3-3y+3y^2=0	$5 x^{2} + y^{3} - 3 y + 3 y^{2} = 0$
81986	Find the Derivative - d/dt	(6t^2-6)/(2t-4)	$\frac{6 t^{2} - 6}{2 t - 4}$
81987	Integrate Using u-Substitution	integral of x^2 square root of x+1 with respect to x	$\int x^{2} \sqrt{x + 1} d x$
81988	Find the Antiderivative	2/( square root of 4x+3)-4/(x^5)	$\frac{2}{\sqrt{4 x + 3}} - \frac{4}{x^{5}}$
81989	Find the Derivative - d/dx	2x natural log of 5x^2	$2 x \ln (5 x^{2})$
81990	Integrate By Parts	integral of 1/(x^2) with respect to x	$\int \frac{1}{x^{2}} d x$
81991	Evaluate the Integral	integral of ( square root of x^3)/2 with respect to x	$\int \frac{\sqrt{x^{3}}}{2} d x$
81992	Evaluate the Integral	integral of 6x(x^2+1)^(3/2) with respect to x	$\int 6 x {(x^{2} + 1)}^{\frac{3}{2}} d x$
81993	Find the Tangent Line at x=1	f(x)=5x-2x^3-2 is concave down at x=1	$f (x) = 5 x - 2 x^{3} - 2$ is concave down at $x = 1$
81994	Find the Inflection Points	f(x)=-3/20x^5+8x^3	$f (x) = - \frac{3}{20} x^{5} + 8 x^{3}$
81995	Evaluate the Integral	integral of (3/(x^4)) with respect to x	$\int (\frac{3}{x^{4}}) d x$
81996	Find the Antiderivative	1/(X^3+X)	$\frac{1}{X^{3} + X}$
81997	Evaluate the Integral	integral from 0 to pi/6 of (3cos(3theta))^2 with respect to theta	$\int_{0}^{\frac{π}{6}} {(3 \cos (3 θ))}^{2} d θ$
81998	Find the Antiderivative	natural log of 2x+1	$\ln (2 x + 1)$
81999	Evaluate the Integral	integral of (3x^2)/( square root of 1-x^6) with respect to x	$\int \frac{3 x^{2}}{\sqrt{1 - x^{6}}} d x$
82000	Find dy/dx	3y^3=5x^2-4y-3y^2	$3 y^{3} = 5 x^{2} - 4 y - 3 y^{2}$