Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
85001	Find the Antiderivative	x/( square root of 2x^2+3)	$\frac{x}{\sqrt{2 x^{2} + 3}}$
85002	Evaluate the Integral	integral from pi/3 to pi/2 of sin(x) with respect to x	$\int_{\frac{π}{3}}^{\frac{π}{2}} \sin (x) d x$
85003	Find the Derivative - d/dk	kx	$k x$
85004	Evaluate the Limit	limit as x approaches infinity of 4/(x+5)	$lim_{x \to \infty} \frac{4}{x + 5}$
85005	Evaluate the Integral	integral from 1 to 2 of (x^2-1)/(x+1) with respect to x	$\int_{1}^{2} \frac{x^{2} - 1}{x + 1} d x$
85006	Find the Antiderivative	(dx)/((3-2x)^5)	$\frac{d x}{{(3 - 2 x)}^{5}}$
85007	Find the Antiderivative	cube root of x(x-4)	$\sqrt[3]{x} (x - 4)$
85008	Find dy/dx	y=5 cube root of -9x-1	$y = 5 \sqrt[3]{- 9 x - 1}$
85009	Find the Maximum/Minimum Value	y=4sin((4pi)/3x)	$y = 4 \sin (\frac{4 π}{3} x)$
85010	Evaluate the Limit	limit as x approaches 2 of (3x^2-6x)/(4-3x)	$lim_{x \to 2} \frac{3 x^{2} - 6 x}{4 - 3 x}$
85011	Find the Derivative - d/dx	y=(e^(-x))/(x+1)	$y = \frac{e^{- x}}{x + 1}$
85012	Find the Derivative - d/dx	6.687(0.931)^x	$6.687 {(0.931)}^{x}$
85013	Find the Integral	x(x^2+9)	$x (x^{2} + 9)$
85014	Evaluate the Limit	limit as x approaches infinity of (6x^3+4x^2+5)/(8x^3+7x-3)	$lim_{x \to \infty} \frac{6 x^{3} + 4 x^{2} + 5}{8 x^{3} + 7 x - 3}$
85015	Find the Antiderivative	(x^2+4)/x	$\frac{x^{2} + 4}{x}$
85016	Find the Derivative - d/dx	10000(1/x+x/(x+3))	$10000 (\frac{1}{x} + \frac{x}{x + 3})$
85017	Solve the Differential Equation	(dy)/(dx)=(3-y)/2	$\frac{d y}{d x} = \frac{3 - y}{2}$
85018	Find Where Increasing/Decreasing	f(x) = square root of 2x+3-2	$f (x) = \sqrt{2 x + 3} - 2$
85019	Find dy/dx	y=xy^2+4x-y	$y = x y^{2} + 4 x - y$
85020	Find the Derivative - d/dx	y=(sin(x)^2)/(cos(x)^2)	$y = \frac{\sin^{2} (x)}{\cos^{2} (x)}$
85021	Find dy/dx	y=2 square root of 6x^2-8x+5	$y = 2 \sqrt{6 x^{2} - 8 x + 5}$
85022	Find dx/dy	3x^2-2xy+5y^2=1	$3 x^{2} - 2 x y + 5 y^{2} = 1$
85023	Integrate By Parts	integral of 4xe^(2x) with respect to x	$\int 4 x e^{2 x} d x$
85024	Evaluate the Limit	limit as x approaches infinity of 2/(x^4)	$lim_{x \to \infty} \frac{2}{x^{4}}$
85025	Find Where Increasing/Decreasing	y = square root of x+1-3	$y = \sqrt{x + 1} - 3$
85026	Evaluate the Integral	2pi integral from 1 to 4 of x(1/(pix)) with respect to x	$2 π \int_{1}^{4} x (\frac{1}{π x}) d x$
85027	Find the Concavity	-3/5x^5+7x^4	$- \frac{3}{5} x^{5} + 7 x^{4}$
85028	Find the Concavity	-1/15x^6+6x^4	$- \frac{1}{15} x^{6} + 6 x^{4}$
85029	Evaluate the Summation	3 sum from m=1 to 4 of -1-m^2	$3 \sum_{m = 1}^{4} - 1 - m^{2}$
85030	Evaluate the Limit	limit as x approaches pi from the right of (7 square root of x)/(csc(x))	$lim_{x \to π^{+}} \frac{7 \sqrt{x}}{\csc (x)}$
85031	Find the Integral	(x^2)/(x^3+1)	$\frac{x^{2}}{x^{3} + 1}$
85032	Find the Maximum/Minimum Value	y=x^2+x+2	$y = x^{2} + x + 2$
85033	Find dy/dx	cos(x+y)=y	$\cos (x + y) = y$
85034	Evaluate the Limit	limit as x approaches 0 of (2x^3+5x^2-10x)/(x^2+2x)	$lim_{x \to 0} \frac{2 x^{3} + 5 x^{2} - 10 x}{x^{2} + 2 x}$
85035	Find the Derivative - d/dt	( natural log of t)^2	$\ln^{2} (t)$
85036	Evaluate the Limit	limit as x approaches 11 from the right of ( square root of x-11)/x	$lim_{x \to 11^{+}} \frac{\sqrt{x - 11}}{x}$
85037	Find the Center and Radius	x^2+y^2+6y=-50-14x	$x^{2} + y^{2} + 6 y = - 50 - 14 x$
85038	Find the Average Value of the Function	f(x)=x^2 , [0,3]	$f (x) = x^{2}$ , $[0, 3]$
85039	Find dy/dx	ax^5+x^3y-y^2x=12	$a x^{5} + x^{3} y - y^{2} x = 12$
85040	Find the Derivative - d/dx	x+27/(2x^2)	$x + \frac{27}{2 x^{2}}$
85041	Evaluate the Limit	limit as x approaches b of ((x-b)^10-4x+4b)/(x-b)	$lim_{x \to b} \frac{{(x - b)}^{10} - 4 x + 4 b}{x - b}$
85042	Evaluate the Integral	integral from 0 to 1 of (1-x^9) with respect to x	$\int_{0}^{1} (1 - x^{9}) d x$
85043	Find the Derivative - d/dx	y=arcsec( square root of 3x^3)	$y = arcsec (\sqrt{3 x^{3}})$
85044	Evaluate the Integral	integral of (5x-1) square root of x with respect to x	$\int (5 x - 1) \sqrt{x} d x$
85045	Evaluate the Summation	3 sum from p=3 to 8 of 5-p	$3 \sum_{p = 3}^{8} 5 - p$
85046	Find the Derivative - d/dx	picos(pix)	$π \cos (π x)$
85047	Evaluate the Limit	limit as x approaches -1 from the right of F(x)	$lim_{x \to {(- 1)}^{+}} F (x)$
85048	Evaluate the Derivative at x=2	y(x)=e^(x^3-8) , x=2	$y (x) = e^{x^{3} - 8}$ , $x = 2$
85049	Find the Center and Radius	x^2-8x+y^2+6x=0	$x^{2} - 8 x + y^{2} + 6 x = 0$
85050	Evaluate the Integral	integral from 0 to k of x/(x^2+4) with respect to x=1/2 natural log of 4	$\int_{0}^{k} \frac{x}{x^{2} + 4} d x = \frac{1}{2} \ln (4)$
85051	Find the Derivative - d/dy	x^4-5x^3y^2+2y^4	$x^{4} - 5 x^{3} y^{2} + 2 y^{4}$
85052	Find the Derivative - d/dx	( square root of 2x^2)/(cos(x))	$\frac{\sqrt{2 x^{2}}}{\cos (x)}$
85053	Find the Derivative - d/dx	(e^(-x))/(-3x)	$\frac{e^{- x}}{- 3 x}$
85054	Evaluate the Limit	limit as x approaches pi from the right of (2 square root of x)/(csc(x))	$lim_{x \to π^{+}} \frac{2 \sqrt{x}}{\csc (x)}$
85055	Evaluate the Integral	integral of (7 square root of x^3+2 cube root of x^2) with respect to x	$\int (7 \sqrt{x^{3}} + 2 \sqrt[3]{x^{2}}) d x$
85056	Find the Derivative - d/dx	natural log of 2/(x^2)	$\ln (\frac{2}{x^{2}})$
85057	Find the Antiderivative	(cos(x))/(sin(x)^5)	$\frac{\cos (x)}{\sin^{5} (x)}$
85058	Find the Percentage Rate of Change	y=1200*(1+0.3)^t	$y = 1200 \cdot {(1 + 0.3)}^{t}$
85059	Find the Derivative - d/dx	integral of square root of x with respect to x	$\int \sqrt{x} d x$
85060	Integrate Using u-Substitution	integral of square root of 9-x^2 with respect to x	$\int \sqrt{9 - x^{2}} d x$
85061	Find dy/dx	2y^2-4=4x^2	$2 y^{2} - 4 = 4 x^{2}$
85062	Find the Maximum/Minimum Value	f(x)=2sin(2x)-pi/2	$f (x) = 2 \sin (2 x) - \frac{π}{2}$
85063	Find dy/dx at (-3,1)	x^2+y^2=2x+y+15 ;, (-3,1)	$x^{2} + y^{2} = 2 x + y + 15$ ;, $(- 3, 1)$
85064	Evaluate the Limit	limit as x approaches negative infinity of (x^2-25)/(x(x-5))	$lim_{x \to - \infty} \frac{x^{2} - 25}{x (x - 5)}$
85065	Find the Maximum/Minimum Value	y=x^3-4x-6	$y = x^{3} - 4 x - 6$
85066	Find the Derivative - d/dx	log of x^2+y^2	$\log (x^{2} + y^{2})$
85067	Evaluate the Limit	limit as x approaches infinity of (x+7)/(x^4+6x)	$lim_{x \to \infty} \frac{(x + 7)}{(x^{4} + 6 x)}$
85068	Evaluate the Integral	integral of (-1/x+7e^x) with respect to x	$\int (- \frac{1}{x} + 7 e^{x}) d x$
85069	Evaluate the Integral	integral from 1 to 27 of ( cube root of x-1/x) with respect to x	$\int_{1}^{27} (\sqrt[3]{x} - \frac{1}{x}) d x$
85070	Find the Antiderivative	e^(-2x)+2x	$e^{- 2 x} + 2 x$
85071	Evaluate the Integral	integral of (3x^3+1+4x^2) with respect to x	$\int (3 x^{3} + 1 + 4 x^{2}) d x$
85072	Evaluate the Integral	integral from 0 to 9 of ( square root of x-1/3x) with respect to x	$\int_{0}^{9} (\sqrt{x} - \frac{1}{3} x) d x$
85073	Find dy/dx	y = cube root of -9x^2-4x	$y = \sqrt[3]{- 9 x^{2} - 4 x}$
85074	Evaluate the Integral	integral from 0 to infinity of 1/(x^2) with respect to x	$\int_{0}^{\infty} \frac{1}{x^{2}} d x$
85075	Find the Inflection Points	-1/6x^4+x^2	$- \frac{1}{6} x^{4} + x^{2}$
85076	Find the Antiderivative	4x+1/(x^2)	$4 x + \frac{1}{x^{2}}$
85077	Evaluate the Limit	limit as x approaches 1 of (x natural log of x)/(x^2-1)	$lim_{x \to 1} \frac{x \ln (x)}{x^{2} - 1}$
85078	Find the Second Derivative	y=-5/3x^4+1/4x^5+4/15	$y = - \frac{5}{3} x^{4} + \frac{1}{4} x^{5} + \frac{4}{15}$
85079	Find the Antiderivative	f(t)=(2t-4+5 square root of t)/( square root of t)	$f (t) = \frac{2 t - 4 + 5 \sqrt{t}}{\sqrt{t}}$
85080	Find the Derivative - d/dx	( natural log of x)/(sin(x))	$\frac{\ln (x)}{\sin (x)}$
85081	Find Where Increasing/Decreasing	f(x)=x^5+x^4	$f (x) = x^{5} + x^{4}$
85082	Find the Antiderivative	x^0	$x^{0}$
85083	Find the Derivative - d/dx	3^4*x^3	$3^{4} \cdot x^{3}$
85084	Find the Derivative - d/dx	2e^x+1	$2 e^{x} + 1$
85085	Evaluate the Integral	integral of u^n with respect to u=(u^2)/2+c	$\int u^{n} d u = \frac{u^{2}}{2} + c$
85086	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x^5)/(e^x)	$lim_{x \to \infty} \frac{x^{5}}{e^{x}}$
85087	Evaluate the Integral	integral of 4cos(theta)cos(sin(theta))^5 with respect to theta	$\int 4 \cos (θ) \cos^{5} (\sin (θ)) d θ$
85088	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 16x^2+x)/x	$lim_{x \to - \infty} \frac{\sqrt{16 x^{2} + x}}{x}$
85089	Find the Second Derivative	f(x)=e^(1/x)	$f (x) = e^{\frac{1}{x}}$
85090	Find the Integral	5e^(5x)dx	$5 e^{5 x} d x$
85091	Find the Antiderivative	f(x)=6/(5 square root of 4x+2)+1/(cos(5x)^2)	$f (x) = \frac{6}{5 \sqrt{4 x + 2}} + \frac{1}{\cos^{2} (5 x)}$
85092	Evaluate the Integral	integral from 1 to 2 of (16(3-2x)^(5/3))/3 with respect to x	$\int_{1}^{2} \frac{16 {(3 - 2 x)}^{\frac{5}{3}}}{3} d x$
85093	Determine if Continuous	f(x)=x^2-c if x<5; 4x+2c if x>=5	$f (x) = {\begin{cases} x^{2} - c & x < 5 \\ 4 x + 2 c & x \geq 5 \end{cases}$
85094	Evaluate the Limit	limit as x approaches 3/2 of (-x-3)/(x^2+x+1)	$lim_{x \to \frac{3}{2}} \frac{- x - 3}{x^{2} + x + 1}$
85095	Find the Derivative - d/dX	6X^2-4Y	$6 X^{2} - 4 Y$
85096	Find the Integral	-6sin(3x)dx	$- 6 \sin (3 x) d x$
85097	Evaluate the Integral	integral of (2x+3)^2e^(x+1) with respect to x	$\int {(2 x + 3)}^{2} e^{x + 1} d x$
85098	Find the Derivative - d/dx	(1+tan(x))/(1+cot(x))	$\frac{1 + \tan (x)}{1 + \cot (x)}$
85099	Evaluate the Integral	integral of ((z^6+3z^4-z^2-3)/( square root of z)) with respect to z	$\int (\frac{z^{6} + 3 z^{4} - z^{2} - 3}{\sqrt{z}}) d z$
85100	Integrate Using u-Substitution	integral of xsin(x/2) with respect to x	$\int x \sin (\frac{x}{2}) d x$