Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
81401	Evaluate the Integral	integral of (5x^4-4x^3+3x^2) with respect to x	$\int (5 x^{4} - 4 x^{3} + 3 x^{2}) d x$
81402	Find the Derivative - d/dx	(4-x^2)/(3- square root of x^2+5)	$\frac{4 - x^{2}}{3 - \sqrt{x^{2} + 5}}$
81403	Evaluate the Integral	integral of 8/( square root of 12-x^2-4x) with respect to x	$\int \frac{8}{\sqrt{12 - x^{2} - 4 x}} d x$
81404	Find dy/dx	y=-8sin(x)	$y = - 8 \sin (x)$
81405	Evaluate the Integral	integral of (3-2x) square root of 9x with respect to x	$\int (3 - 2 x) \sqrt{9 x} d x$
81406	Find the Derivative - d/dx	( natural log of (x)^2)/x	$\frac{\ln ({(x)}^{2})}{x}$
81407	Find the Antiderivative	f(x) = square root of x-x^(3/4)+1/x	$f (x) = \sqrt{x} - x^{\frac{3}{4}} + \frac{1}{x}$
81408	Find the Antiderivative	(10t^-3+12t^-9+4t^3)dt	$(10 t^{- 3} + 12 t^{- 9} + 4 t^{3}) d t$
81409	Find Where Increasing/Decreasing	f(x)=(3/2)^(-x)-7	$f (x) = {(\frac{3}{2})}^{- x} - 7$
81410	Find the Derivative - d/dx	(x/2)	$(\frac{x}{2})$
81411	Find the Slope of the Tangent Line at x=1	e^x+100e+8x^4+49 at x=1	$e^{x} + 100 e + 8 x^{4} + 49$ at $x = 1$
81412	Solve the Differential Equation	y'-y^2=0	$y' - y^{2} = 0$
81413	Find dy/dx	-xy-4y^2+5=0	$- x y - 4 y^{2} + 5 = 0$
81414	Find the Maximum/Minimum Value	g(x)=3x^4+8x^3+4	$g (x) = 3 x^{4} + 8 x^{3} + 4$
81415	Evaluate from the Left	limit as x approaches 2 of 2x+1	$lim_{x \to 2} 2 x + 1$
81416	Find dy/dx	-xy+5+5y^2=0	$- x y + 5 + 5 y^{2} = 0$
81417	Evaluate the Integral	integral from 0 to pi/6 of sec(2x)tan(2x) with respect to x	$\int_{0}^{\frac{π}{6}} \sec (2 x) \tan (2 x) d x$
81418	Find the Derivative - d/dx	y=5x^4(7x^5)	$y = 5 x^{4} (7 x^{5})$
81419	Find dy/dx	-y^3-5y-3y^2-5x^3=x^2	$- y^{3} - 5 y - 3 y^{2} - 5 x^{3} = x^{2}$
81420	Evaluate the Integral	integral of 1/(5+2x^6)(12x^5) with respect to x	$\int \frac{1}{5 + 2 x^{6}} (12 x^{5}) d x$
81421	Find Where Increasing/Decreasing	f(x)=x^(1/5)	$f (x) = x^{\frac{1}{5}}$
81422	Find the Derivative - d/dx	6-\|6-4x\|	$6 - \| 6 - 4 x \|$
81423	Find the Maximum/Minimum Value	y=-3 square root of x+1+4	$y = - 3 \sqrt{x + 1} + 4$
81424	Find the Maximum/Minimum Value	y=xe^x	$y = x e^{x}$
81425	Evaluate the Limit	limit as x approaches infinity of square root of (25x^2)/(4+36x^2)	$lim_{x \to \infty} \sqrt{\frac{25 x^{2}}{4 + 36 x^{2}}}$
81426	Evaluate the Integral	integral of (5e^(2x)+1/x) with respect to x	$\int (5 e^{2 x} + \frac{1}{x}) d x$
81427	Find the Antiderivative	e^(2x)dx	$e^{2 x} d x$
81428	Evaluate the Integral	integral of (9-7x^(3/2))/(-7x^(2/3)) with respect to x	$\int \frac{9 - 7 x^{\frac{3}{2}}}{- 7 x^{\frac{2}{3}}} d x$
81429	Find the Skew	1 , 4 , 14	$1$ , $4$ , $14$
81430	Find the Skew	10 , 74 , 78 , 102	$10$ , $74$ , $78$ , $102$
81431	Find the Antiderivative	1/((2x+1)^3)	$\frac{1}{{(2 x + 1)}^{3}}$
81432	Find the Derivative - d/dx	cos(x)^2-cos(x)	$\cos^{2} (x) - \cos (x)$
81433	Find dy/dx	-y^2-x^2y-x^2=-2	$- y^{2} - x^{2} y - x^{2} = - 2$
81434	Evaluate the Limit	limit as x approaches 0 of e^(4x)-2e^(2x)+1	$lim_{x \to 0} e^{4 x} - 2 e^{2 x} + 1$
81435	Find the Derivative - d/dx	x+ square root of 7x-3	$x + \sqrt{7 x - 3}$
81436	Find the Antiderivative	(x(2+x))/((x+1)^2)	$\frac{x (2 + x)}{{(x + 1)}^{2}}$
81437	Find the Derivative - d/dx	x^3-x^2cos(x)	$x^{3} - x^{2} \cos (x)$
81438	Find the Average Value of the Function	f(x)=-4/(x-2) , [0,1]	$f (x) = - \frac{4}{x - 2}$ , $[0, 1]$
81439	Find the Second Derivative	y=-1/4x^-4-1/16+1/4x^4	$y = - \frac{1}{4} x^{- 4} - \frac{1}{16} + \frac{1}{4} x^{4}$
81440	Find the Integral	(x^2)/(x^2+1)	$\frac{x^{2}}{x^{2} + 1}$
81441	Find the Derivative - d/dx	4x^2e^(x^2)+2e^(x^2)	$4 x^{2} e^{x^{2}} + 2 e^{x^{2}}$
81442	Find the Derivative - d/dx	y = square root of 5x	$y = \sqrt{5} x$
81443	Find Where Increasing/Decreasing	f(x)=((x+1)^2)/(x-4)	$f (x) = \frac{{(x + 1)}^{2}}{x - 4}$
81444	Evaluate the Limit	limit as x approaches 0 of (1+x)/(4x-1)	$lim_{x \to 0} \frac{1 + x}{4 x - 1}$
81445	Find the Antiderivative	( square root of x)/(x^2)	$\frac{\sqrt{x}}{x^{2}}$
81446	Solve the Differential Equation	y'=yx^3	$y' = y x^{3}$
81447	Find dy/dx	square root of x+y=x	$\sqrt{x + y} = x$
81448	Find the Derivative - d/dt	10-1/5(t-6)^2	$10 - \frac{1}{5} {(t - 6)}^{2}$
81449	Evaluate the Integral	integral of ((2x^3+5x^2-2x)/x) with respect to x	$\int (\frac{2 x^{3} + 5 x^{2} - 2 x}{x}) d x$
81450	Find the Derivative Using Chain Rule - d/dx	y=((3x-1)/(x^2+3))^2	$y = {(\frac{3 x - 1}{x^{2} + 3})}^{2}$
81451	Find the Inflection Points	f(x)=-1/6x^4+x^3+18x^2	$f (x) = - \frac{1}{6} x^{4} + x^{3} + 18 x^{2}$
81452	Find the Center and Radius	3x^2+3y^2-6y+12x=24	$3 x^{2} + 3 y^{2} - 6 y + 12 x = 24$
81453	Find the Integral	e^(x+1)	$e^{x + 1}$
81454	Find dy/dx	e^(xy)+ natural log of xy=3	$e^{x y} + \ln (x y) = 3$
81455	Find the Derivative - d/dx	y=arccos( square root of 1-x)	$y = \arccos (\sqrt{1 - x})$
81456	Find the Concavity	-1/6x^6+2x^5-5x^4	$- \frac{1}{6} x^{6} + 2 x^{5} - 5 x^{4}$
81457	Integrate Using u-Substitution	integral of cos(3x) with respect to x	$\int \cos (3 x) d x$
81458	Find dy/dx	-5+x^2+y^3-y=0	$- 5 + x^{2} + y^{3} - y = 0$
81459	Evaluate the Integral	integral from negative infinity to 5 of 1/(x^4) with respect to x	$\int_{- \infty}^{5} \frac{1}{x^{4}} d x$
81460	Evaluate the Integral	integral from 0 to 1 of x*7^x with respect to x	$\int_{0}^{1} x \cdot 7^{x} d x$
81461	Evaluate the Integral	integral from 1 to infinity of x/((1+x^2)^2) with respect to x	$\int_{1}^{\infty} \frac{x}{{(1 + x^{2})}^{2}} d x$
81462	Evaluate the Integral	integral of (2^x+1) with respect to x	$\int (2^{x} + 1) d x$
81463	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^(-x)-1)/(3sin(-x)+3x)	$lim_{x \to 0} \frac{e^{- x} - 1}{3 \sin (- x) + 3 x}$
81464	Evaluate the Integral	integral from 0 to 5 of (f(x)+g(x)) with respect to x	$\int_{0}^{5} (f (x) + g (x)) d x$
81465	Find the Derivative - d/dx	d/(dx)(ke^(-2x)-2x^(k^2))	$\frac{d}{d x} (k e^{- 2 x} - 2 x^{k^{2}})$
81466	Find the Antiderivative	(e^x-e^(-x))/(e^x+e^(-x))	$\frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}$
81467	Evaluate the Integral	integral of 2x(2x+3)^2 with respect to x	$\int 2 x {(2 x + 3)}^{2} d x$
81468	Evaluate the Integral	integral from 1 to 4 of ( square root of 2+ square root of x)/( square root of x) with respect to x	$\int_{1}^{4} \frac{(\sqrt{2 + \sqrt{x}})}{\sqrt{x}} d x$
81469	Find dy/dx	5x^2-x^3-2y^3-y^2=3x	$5 x^{2} - x^{3} - 2 y^{3} - y^{2} = 3 x$
81470	Find the Antiderivative	x* square root of x	$x \cdot \sqrt{x}$
81471	Find dy/dx	-4y^2-x-xy=0	$- 4 y^{2} - x - x y = 0$
81472	Find the Antiderivative	1/(x^3)dx	$\frac{1}{x^{3}} d x$
81473	Find dy/dx	y-x^2=-2+xy^2	$y - x^{2} = - 2 + x y^{2}$
81474	Find the Antiderivative	f(x)=2(x-1)^2	$f (x) = 2 {(x - 1)}^{2}$
81475	Find dy/dx	x^3y+x^3=-y^2	$x^{3} y + x^{3} = - y^{2}$
81476	Evaluate the Integral	2pi integral from 0 to 4 of x^3 with respect to x	$2 π \int_{0}^{4} x^{3} d x$
81477	Find the Antiderivative	f(x)=2sin(x)+x^2	$f (x) = 2 \sin (x) + x^{2}$
81478	Find the Antiderivative	x-x^2	$x - x^{2}$
81479	Find the Center and Radius	(y^2)/9-(x+4)^2=1	$\frac{y^{2}}{9} - {(x + 4)}^{2} = 1$
81480	Find dy/dx	5-y^3=xy	$5 - y^{3} = x y$
81481	Find the Derivative - d/dx	1/(1+sin(x))	$\frac{1}{1 + \sin (x)}$
81482	Find the Percentage Rate of Change	h(t)=1250(0.865)^t	$h (t) = 1250 {(0.865)}^{t}$
81483	Find the Antiderivative	f(x)=tan(x)	$f (x) = \tan (x)$
81484	Find the Antiderivative	f(x)=1/(2 square root of x)-1/(x^2)	$f (x) = \frac{1}{2 \sqrt{x}} - \frac{1}{x^{2}}$
81485	Find the Derivative - d/dx	y=(2tan(2x)^3-1)^(1/3)	$y = {(2 \tan^{3} (2 x) - 1)}^{\frac{1}{3}}$
81486	Find the Maximum/Minimum Value	f(x)=-x^4+4x^2-x-2	$f (x) = - x^{4} + 4 x^{2} - x - 2$
81487	Find the Antiderivative	f(x)=4x+3+5x^3	$f (x) = 4 x + 3 + 5 x^{3}$
81488	Find dy/dx	1+4x^3=5y^2	$1 + 4 x^{3} = 5 y^{2}$
81489	Use Logarithmic Differentiation to Find the Derivative	y=x^(5sin(x))	$y = x^{5 \sin (x)}$
81490	Find the Maximum/Minimum Value	f(x)=(x^2-1)/x	$f (x) = \frac{x^{2} - 1}{x}$
81491	Find the Antiderivative	1/(x^2-2x)	$\frac{1}{x^{2} - 2 x}$
81492	Integrate Using u-Substitution	integral of x square root of 1-x with respect to x	$\int x \sqrt{1 - x} d x$
81493	Find the Average Value of the Function	f(x)=x^2 , [0,2]	$f (x) = x^{2}$ , $[0, 2]$
81494	Find Where Increasing/Decreasing	f(x)=((x-2)^3)/x	$f (x) = \frac{{(x - 2)}^{3}}{x}$
81495	Evaluate the Integral	integral from 0 to 1/4 of (8x)/( square root of 1-4x^2) with respect to x	$\int_{0}^{\frac{1}{4}} \frac{8 x}{\sqrt{1 - 4 x^{2}}} d x$
81496	Evaluate the Integral	integral of ((3x^3-4x-2)/(x^3)) with respect to x	$\int (\frac{3 x^{3} - 4 x - 2}{x^{3}}) d x$
81497	Find Where Increasing/Decreasing	(x+3)/(x^2)	$\frac{(x + 3)}{x^{2}}$
81498	Find the Antiderivative	f(x)=4+2x^6+x^2	$f (x) = 4 + 2 x^{6} + x^{2}$
81499	Find the Derivative - d/dx	x^2cos(x^2)	$x^{2} \cos (x^{2})$
81500	Evaluate the Integral	integral of x^2(3+x)^2 with respect to x	$\int x^{2} {(3 + x)}^{2} d x$