Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
82901	Integrate Using u-Substitution	integral of (x^9)/(1+x^20) with respect to x	$\int \frac{x^{9}}{1 + x^{20}} d x$
82902	Find the Derivative - d/dx	-x^2-xy+y^2-1	$- x^{2} - x y + y^{2} - 1$
82903	Evaluate the Integral	integral of x(x^2+7)(1/3) with respect to x	$\int x (x^{2} + 7) (\frac{1}{3}) d x$
82904	Find Where Increasing/Decreasing	f'(x)=((x+1)^2)/(x-4)	$f' (x) = \frac{{(x + 1)}^{2}}{x - 4}$
82905	Evaluate the Integral	integral of (x^7 square root of x)/(x^5)-3 cube root of x+5x^4-1/(2x)+e^x+2021 with respect to x	$\int \frac{x^{7} \sqrt{x}}{x^{5}} - 3 \sqrt[3]{x} + 5 x^{4} - \frac{1}{2 x} + e^{x} + 2021 d x$
82906	Find dy/dx	x^2+y^2=x	$x^{2} + y^{2} = x$
82907	Find the Maximum/Minimum Value	x^5(x+1)(x-1)	$x^{5} (x + 1) (x - 1)$
82908	Find the Derivative - d/dx	y=e^x+e^(-x)	$y = e^{x} + e^{- x}$
82909	Evaluate the Limit	limit as x approaches 1/2 of (2-4x)/(8-64x^3)	$lim_{x \to \frac{1}{2}} \frac{2 - 4 x}{8 - 64 x^{3}}$
82910	Find the Derivative - d/dx	natural log of (e^(x^3))/(x^4-7x+1)	$\ln (\frac{e^{x^{3}}}{x^{4} - 7 x + 1})$
82911	Evaluate the Limit	limit as x approaches negative infinity of ( square root of 25x^2-7)/(x+2) is	$lim_{x \to - \infty} \frac{\sqrt{25 x^{2} - 7}}{x + 2}$ is
82912	Find the Maximum/Minimum Value	h(t)=60-55sin(pi/10t+pi/2)	$h (t) = 60 - 55 \sin (\frac{π}{10} t + \frac{π}{2})$
82913	Integrate Using u-Substitution	integral of (x^3)/((1+x^4)^2) with respect to x	$\int \frac{x^{3}}{{(1 + x^{4})}^{2}} d x$
82914	Evaluate the Limit	limit as x approaches infinity of ((x+1)/(x-1))^x	$lim_{x \to \infty} {(\frac{x + 1}{x - 1})}^{x}$
82915	Integrate Using u-Substitution	integral of x square root of x-2 with respect to x	$\int x \sqrt{x - 2} d x$
82916	Find the Antiderivative	11*4x^3	$11 \cdot 4 x^{3}$
82917	Evaluate the Integral	integral of x^5e^(1-x^6) with respect to x	$\int x^{5} e^{1 - x^{6}} d x$
82918	Evaluate the Integral	integral of (8x^4+18x^3-7x)/x with respect to x	$\int \frac{8 x^{4} + 18 x^{3} - 7 x}{x} d x$
82919	Integrate Using u-Substitution	integral of (x^2-9)^3(2x) with respect to x	$\int {(x^{2} - 9)}^{3} (2 x) d x$
82920	Find the Critical Points	Let h(x)=(e^x)/(x-1)	Let $h (x) = \frac{e^{x}}{x - 1}$
82921	Find the Minimum	y=x^2	$y = x^{2}$
82922	Find the Derivative - d/dx	(2x^3+x^2-6x)^(2/3)	${(2 x^{3} + x^{2} - 6 x)}^{\frac{2}{3}}$
82923	Evaluate the Limit	Calculate limit as x approaches 1 of (x^2-1)/(x-1)	Calculate $lim_{x \to 1} \frac{x^{2} - 1}{x - 1}$
82924	Evaluate the Limit	limit as x approaches 0 of (4sin(x/4))/x	$lim_{x \to 0} \frac{4 \sin (\frac{x}{4})}{x}$
82925	Find the Derivative - d/dx	square root of x/y	$\sqrt{\frac{x}{y}}$
82926	Find the Derivative - d/dx	d/(dx)(x^2*sin(x))	$\frac{d}{d x} (x^{2} \cdot \sin (x))$
82927	Find the Derivative - d/dx	(x^(n+1))/(n+1)	$\frac{x^{n + 1}}{n + 1}$
82928	Find the Second Derivative	3x^(2/3)-2x	$3 x^{\frac{2}{3}} - 2 x$
82929	Find the Derivative - d/dx	y=1+2xe^y	$y = 1 + 2 x e^{y}$
82930	Find the Antiderivative	e^x(1-3e^(-2x))	$e^{x} (1 - 3 e^{- 2 x})$
82931	Evaluate Using L'Hospital's Rule	limit as x approaches -1 of (2x^2+2x)/(3cos(-1-x)-3)	$lim_{x \to - 1} \frac{2 x^{2} + 2 x}{3 \cos (- 1 - x) - 3}$
82932	Find the Antiderivative	4/( square root of x)+3/x-2e^x	$\frac{4}{\sqrt{x}} + \frac{3}{x} - 2 e^{x}$
82933	Find the Center and Radius	(x-4)^2+(y+3)=25	${(x - 4)}^{2} + (y + 3) = 25$
82934	Find the Antiderivative	(2x^2+5)/(x^2+1)	$\frac{2 x^{2} + 5}{x^{2} + 1}$
82935	Evaluate the Integral	integral from 3 to 6 of 1/( square root of 6x-x^2) with respect to x	$\int_{3}^{6} \frac{1}{\sqrt{6 x - x^{2}}} d x$
82936	Find the Inflection Points	f(x)=arctan(x^2)	$f (x) = \arctan (x^{2})$
82937	Find the Derivative - d/du	arctan(u)	$\arctan (u)$
82938	Evaluate the Integral	integral from 0 to 1 of natural log of 1-x with respect to x	$\int_{0}^{1} \ln (1 - x) d x$
82939	Evaluate the Integral	integral from 0 to 5 of (x-2)^2+1 with respect to x	$\int_{0}^{5} {(x - 2)}^{2} + 1 d x$
82940	Find dy/dx	5y^3+xy+x^3+3=0	$5 y^{3} + x y + x^{3} + 3 = 0$
82941	Find the Integral	2sin(x)^2	$2 \sin^{2} (x)$
82942	Find the Antiderivative	f(x)=1-sin(4x)	$f (x) = 1 - \sin (4 x)$
82943	Evaluate Using Summation Formulas	sum from i=1 to 3 of 1/(x_i^2)	$\sum_{i = 1}^{3} \frac{1}{{x_{i}}^{2}}$
82944	Find the Antiderivative	1/2e^x	$\frac{1}{2} e^{x}$
82945	Evaluate the Limit	limit as x approaches -10 of (1/(-9x-3)-1/87)/(1/(-9x-9)-1/81)	$lim_{x \to - 10} \frac{\frac{1}{- 9 x - 3} - \frac{1}{87}}{\frac{1}{- 9 x - 9} - \frac{1}{81}}$
82946	Find Where Increasing/Decreasing	f(x)=3^(x-2)+1	$f (x) = 3^{x - 2} + 1$
82947	Find the Antiderivative	f(x)=4xe^(2x)	$f (x) = 4 x e^{2 x}$
82948	Evaluate the Integral	integral of (1/( fifth root of x^3)) with respect to x	$\int (\frac{1}{\sqrt[5]{x^{3}}}) d x$
82949	Find the Antiderivative	y=1/(x^2)	$y = \frac{1}{x^{2}}$
82950	Evaluate Using L'Hospital's Rule	limit as x approaches -2 of ( natural log of 3x+7-2x^3)/(3tan(-4-2x)-3x^3)	$lim_{x \to - 2} \frac{\ln (3 x + 7) - 2 x^{3}}{3 \tan (- 4 - 2 x) - 3 x^{3}}$
82951	Find the Maximum/Minimum Value	f(x)=x^4-4x^3+2x^2+x+4	$f (x) = x^{4} - 4 x^{3} + 2 x^{2} + x + 4$
82952	Find the Antiderivative	5x( square root of x-x^2)	$5 x (\sqrt{x} - x^{2})$
82953	Find dy/dx	-5y^3=-2x-xy	$- 5 y^{3} = - 2 x - x y$
82954	Evaluate the Integral	limit as x approaches infinity of 1/( square root of x) integral from 1 to x of 1/( square root of t) with respect to t	$lim_{x \to \infty} \frac{1}{\sqrt{x}} \int_{1}^{x} \frac{1}{\sqrt{t}} d t$
82955	Evaluate the Integral	integral from 0 to infinity of 1/(4x^2+9) with respect to x	$\int_{0}^{\infty} \frac{1}{4 x^{2} + 9} d x$
82956	Evaluate the Integral	2 integral from 1 to 2 of (x^2+1) with respect to x	$2 \int_{1}^{2} (x^{2} + 1) d x$
82957	Find the Antiderivative	e^( natural log of x)	$e^{\ln (x)}$
82958	Find the Domain and Range	f(x)=x+2 if x<=-1; x^2 if x>-1	$f (x) = {\begin{cases} x + 2 & x \leq - 1 \\ x^{2} & x > - 1 \end{cases}$
82959	Find the Derivative - d/dx	2 natural log of sec(x)	$2 \ln (\sec (x))$
82960	Find the Derivative - d/dx	y=9x^(5/2)-7x^(3/2)	$y = 9 x^{\frac{5}{2}} - 7 x^{\frac{3}{2}}$
82961	Evaluate the Integral	integral of 2x(4x+5)(2x+1) with respect to x	$\int 2 x (4 x + 5) (2 x + 1) d x$
82962	Find the Antiderivative	f(x)=7-3(1+x^2)^-1	$f (x) = 7 - 3 {(1 + x^{2})}^{- 1}$
82963	Find the Derivative - d/dx	y=(1+x^2)arctan(x)-x	$y = (1 + x^{2}) \arctan (x) - x$
82964	Evaluate the Integral	integral of (2x^3 natural log of (3+x^4)^4)/(3+x^4) with respect to x	$\int \frac{2 x^{3} \ln ({(3 + x^{4})}^{4})}{3 + x^{4}} d x$
82965	Find the Antiderivative	f(x)=3x^2+sin(x)	$f (x) = 3 x^{2} + \sin (x)$
82966	Find the Concavity	-1/10x^5-2x^4-12x^3	$- \frac{1}{10} x^{5} - 2 x^{4} - 12 x^{3}$
82967	Evaluate the Integral	integral of 2x^2(x+2)^2 with respect to x	$\int 2 x^{2} {(x + 2)}^{2} d x$
82968	Find the Maximum/Minimum Value	y = square root of x+4-1	$y = \sqrt{x + 4} - 1$
82969	Integrate Using u-Substitution	integral of x^5 square root of 2x^6+3 with respect to x	$\int x^{5} \sqrt{2 x^{6} + 3} d x$
82970	Evaluate the Integral	integral from 0 to 4 of pi( square root of x)^2 with respect to x	$\int_{0}^{4} π {(\sqrt{x})}^{2} d x$
82971	Integrate Using u-Substitution	integral of (sin(x))/(cos(x)) with respect to x	$\int \frac{\sin (x)}{\cos (x)} d x$
82972	Evaluate the Integral	integral of (3x^2+4x+1)/(3x^3+6x^2+3x+5) with respect to x	$\int \frac{3 x^{2} + 4 x + 1}{3 x^{3} + 6 x^{2} + 3 x + 5} d x$
82973	Find the Derivative - d/da	pi/(ab)	$\frac{π}{a b}$
82974	Find the Derivative - d/dx	y=(4 square root of x)/(x-2)	$y = \frac{4 \sqrt{x}}{x - 2}$
82975	Find dy/dx	-y+y^2-4y^3+x^2=0	$- y + y^{2} - 4 y^{3} + x^{2} = 0$
82976	Find the Derivative - d/dx	x^3y^2-4xy+5y^3	$x^{3} y^{2} - 4 x y + 5 y^{3}$
82977	Evaluate the Integral	integral of 1/(6 fourth root of x) with respect to x	$\int \frac{1}{6 \sqrt[4]{x}} d x$
82978	Evaluate the Limit	limit as x approaches 2 of (x^3+x^2-5x-3)^3	$lim_{x \to 2} {(x^{3} + x^{2} - 5 x - 3)}^{3}$
82979	Find dy/dx	3x-2y^3+2x^2=0	$3 x - 2 y^{3} + 2 x^{2} = 0$
82980	Find the Derivative - d/dy	-1/(y^2)	$- \frac{1}{y^{2}}$
82981	Evaluate the Limit	limit as x approaches pi/2 of (3cos(x))/(2x-pi)	$lim_{x \to \frac{π}{2}} \frac{3 \cos (x)}{2 x - π}$
82982	Find the Derivative of the Integral	integral from 0 to x of (1+2t+3t^2+4t^3) with respect to t	$\int_{0}^{x} (1 + 2 t + 3 t^{2} + 4 t^{3}) d t$
82983	Evaluate the Integral	integral from -1 to 1 of (1+ square root of 1-x^2) with respect to x	$\int_{- 1}^{1} (1 + \sqrt{1 - x^{2}}) d x$
82984	Find dy/dx	y=arcsec( square root of 3x^3)	$y = arcsec (\sqrt{3 x^{3}})$
82985	Find Where Increasing/Decreasing	f(x)=x+2	$f (x) = x + 2$
82986	Find the Derivative - d/dx	18/( cube root of x-2)	$\frac{18}{\sqrt[3]{x - 2}}$
82987	Evaluate the Integral	integral from -1 to 3 of -3/32x^2+3/16x+9/32 with respect to x	$\int_{- 1}^{3} - \frac{3}{32} x^{2} + \frac{3}{16} x + \frac{9}{32} d x$
82988	Evaluate the Integral	integral of (6/(x^2)-5e^x+sec(x)tan(x)) with respect to x	$\int (\frac{6}{x^{2}} - 5 e^{x} + \sec (x) \tan (x)) d x$
82989	Evaluate the Limit	limit as x approaches -1 of ( square root of x^2+3-2)/(x^2+1)	$lim_{x \to - 1} \frac{\sqrt{x^{2} + 3} - 2}{x^{2} + 1}$
82990	Evaluate the Limit	limit as x approaches 4 of (-5x^2+21x-4)/(24-6x)	$lim_{x \to 4} \frac{- 5 x^{2} + 21 x - 4}{24 - 6 x}$
82991	Evaluate the Integral	integral from -2 to 3 of [y-(y^2-6)] with respect to y	$\int_{- 2}^{3} [y - (y^{2} - 6)] d y$
82992	Use the Initial Value to Solve for c	y'=3x^2 , y=x^3-4+c , y(0)=5	$y' = 3 x^{2}$ , $y = x^{3} - 4 + c$ , $y (0) = 5$
82993	Find the Antiderivative	e^x-2x	$e^{x} - 2 x$
82994	Evaluate the Integral	integral of (1/7-1/(y^(5/4))) with respect to y	$\int (\frac{1}{7} - \frac{1}{y^{\frac{5}{4}}}) d y$
82995	Find dy/dx	x^2y+4y=8	$x^{2} y + 4 y = 8$
82996	Find the Derivative - d/dx	arccos(-x/5)	$\arccos (- \frac{x}{5})$
82997	Find the Derivative - d/dx	y=e^(cot(8x))	$y = e^{\cot (8 x)}$
82998	Evaluate the Limit	limit as x approaches infinity of (1-x)/(2+5x)	$lim_{x \to \infty} \frac{1 - x}{2 + 5 x}$
82999	Evaluate the Limit	limit as x approaches 1 of ((x-1)(x-2))/((x-1)^3)	$lim_{x \to 1} \frac{(x - 1) (x - 2)}{{(x - 1)}^{3}}$
83000	Find the Derivative - d/dx	e^( square root of cos(x))	$e^{\sqrt{\cos (x)}}$