Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
1801	Find the Antiderivative	f(x)=sin(x)	$f (x) = \sin (x)$
1802	Find the Antiderivative	f(x)=1/(x^2)	$f (x) = \frac{1}{x^{2}}$
1803	Find the Antiderivative	e^(x/2)	$e^{\frac{x}{2}}$
1804	Find the Derivative - d/dx	x^9cos(x)	$x^{9} \cos (x)$
1805	Find the Antiderivative	e^(x^2)	$e^{x^{2}}$
1806	Find the Antiderivative	8x	$8 x$
1807	Find the Antiderivative	2e^x	$2 e^{x}$
1808	Find the Local Maxima and Minima	f(x)=x/(x^2+9)	$f (x) = \frac{x}{x^{2} + 9}$
1809	Find the Derivative - d/d@VAR	f(x)=4/(x^2)	$f (x) = \frac{4}{x^{2}}$
1810	Find the Derivative - d/d@VAR	f(x)=tan(x)	$f (x) = \tan (x)$
1811	Find the Derivative - d/d@VAR	f(x)=8x^2	$f (x) = 8 x^{2}$
1812	Find the Derivative - d/d@VAR	f(x)=sin(x)^2	$f (x) = \sin^{2} (x)$
1813	Find the Local Maxima and Minima	f(x)=x+49/x	$f (x) = x + \frac{49}{x}$
1814	Find the Derivative - d/dx	d/(dx)(x^3)	$\frac{d}{d x} (x^{3})$
1815	Find the Local Maxima and Minima	f(x)=x^4-8x^3	$f (x) = x^{4} - 8 x^{3}$
1816	Find the Local Maxima and Minima	f(x)=2x^3+3x^2-12x	$f (x) = 2 x^{3} + 3 x^{2} - 12 x$
1817	Evaluate the Integral	integral of te^(-9t) with respect to t	$\int t e^{- 9 t} d t$
1818	Evaluate the Limit	limit as x approaches 4 of (x^2-4x)/(x^2-3x-4)	$lim_{x \to 4} \frac{x^{2} - 4 x}{x^{2} - 3 x - 4}$
1819	Evaluate the Limit	limit as x approaches 3 of x^2	$lim_{x \to 3} x^{2}$
1820	Evaluate the Limit	limit as x approaches 2 of (2-x)/(x^2-4)	$lim_{x \to 2} \frac{2 - x}{x^{2} - 4}$
1821	Evaluate the Limit	limit as x approaches 0 of cos(1/X)	$lim_{x \to 0} \cos (\frac{1}{X})$
1822	Evaluate the Limit	limit as x approaches infinity of square root of 25x^2+x-5x	$lim_{x \to \infty} \sqrt{25 x^{2} + x} - 5 x$
1823	Evaluate the Limit	limit as x approaches 5 of (x^2-5x+6)/(x-5)	$lim_{x \to 5} \frac{x^{2} - 5 x + 6}{x - 5}$
1824	Evaluate the Limit	limit as x approaches 16 of ( square root of x-4)/(x-16)	$lim_{x \to 16} \frac{\sqrt{x} - 4}{x - 16}$
1825	Evaluate the Integral	integral from 4 to 5 of (x^3-3x^2-9)/(x^3-3x^2) with respect to x	$\int_{4}^{5} \frac{x^{3} - 3 x^{2} - 9}{x^{3} - 3 x^{2}} d x$
1826	Graph	sec(x)	$\sec (x)$
1827	Evaluate the Derivative at @POINT	y=2x^3-5x , (1,-3)	$y = 2 x^{3} - 5 x$ , $(1, - 3)$
1828	Evaluate	arctan(- square root of 3)	$\arctan (- \sqrt{3})$
1829	Find the Critical Points	f(x)=x^4-2x^3	$f (x) = x^{4} - 2 x^{3}$
1830	Find the Critical Points	f(x)=x^4-4x^3+10	$f (x) = x^{4} - 4 x^{3} + 10$
1831	Find the Critical Points	f(x)=3x^(2/3)-2x	$f (x) = 3 x^{\frac{2}{3}} - 2 x$
1832	Find the Critical Points	f(x)=(x^2-4)^(2/3)	$f (x) = {(x^{2} - 4)}^{\frac{2}{3}}$
1833	Find dy/dx	xy=32	$x y = 32$
1834	Evaluate	sin((7pi)/4)	$\sin (\frac{7 π}{4})$
1835	Evaluate	sec(pi/3)tan(pi/3)	$\sec (\frac{π}{3}) \tan (\frac{π}{3})$
1836	Evaluate	arctan(0)	$\arctan (0)$
1837	Find the Horizontal Tangent Line	y=x^2+2x	$y = x^{2} + 2 x$
1838	Find the Horizontal Tangent Line	x^2+y^2=-18x	$x^{2} + y^{2} = - 18 x$
1839	Find the Horizontal Tangent Line	x^2+y^2=-16x	$x^{2} + y^{2} = - 16 x$
1840	Find the Inflection Points	f(x)=x^4-6x^2	$f (x) = x^{4} - 6 x^{2}$
1841	Use the Limit Definition to Find the Derivative	1/x	$\frac{1}{x}$
1842	Use the Limit Definition to Find the Derivative	x^2	$x^{2}$
1843	Use the Limit Definition to Find the Derivative	g(x)=9-x^2	$g (x) = 9 - x^{2}$
1844	Evaluate the Limit	limit as x approaches -1 of (x^2-4x)/(x^2-3x-4)	$lim_{x \to - 1} \frac{x^{2} - 4 x}{x^{2} - 3 x - 4}$
1845	Find the Derivative - d/dx	square root of x	sqrt $(x)$
1846	Find the Derivative - d/dx	(4x)/((x^2+1)^2)	$\frac{4 x}{{(x^{2} + 1)}^{2}}$
1847	Evaluate the Summation	sum from i=1 to 8 of 2^(i-1)	$\sum_{i = 1}^{8} 2^{i - 1}$
1848	Find the Derivative - d/dx	5/(3x)	$\frac{5}{3 x}$
1849	Find the Derivative - d/dx	5x^2-x^3	$5 x^{2} - x^{3}$
1850	Find the Derivative of the Integral	integral of 5x with respect to x	$\int 5 x d x$
1851	Evaluate the Limit	limit as x approaches 2 of square root of (5x^2+5)/(9x-2)	$lim_{x \to 2} \sqrt{\frac{5 x^{2} + 5}{9 x - 2}}$
1852	Evaluate the Integral	integral of x cube root of 6x+7 with respect to x	$\int x \sqrt[3]{6 x + 7} d x$
1853	Evaluate	-(3(-3)^2(-5))/(2(-3)^3-(-5))	$- \frac{3 {(- 3)}^{2} (- 5)}{2 {(- 3)}^{3} - (- 5)}$
1854	Evaluate the Integral	integral from 1 to 8 of 1/(x^3) with respect to x	$\int_{1}^{8} \frac{1}{x^{3}} d x$
1855	Evaluate the Integral	integral of 5x^2 with respect to x	$\int 5 x^{2} d x$
1856	Evaluate the Integral	integral of 1/u with respect to u	$\int \frac{1}{u} d u$
1857	Evaluate the Integral	integral of 1/y with respect to y	$\int \frac{1}{y} d y$
1858	Evaluate the Integral	integral of natural log of 4x-3 with respect to x	$\int \ln (4 x - 3) d x$
1859	Evaluate the Integral	integral from 0 to 7 of square root of y+9 with respect to y	$\int_{0}^{7} \sqrt{y + 9} d y$
1860	Evaluate the Integral	integral from 0 to natural log of 2 of e^x with respect to x	$\int_{0}^{\ln (2)} e^{x} d x$
1861	Evaluate the Integral	integral from 0 to 1 of xe^x with respect to x	$\int_{0}^{1} x e^{x} d x$
1862	Evaluate the Integral	integral from 0 to 1 of 3x with respect to x	$\int_{0}^{1} 3 x d x$
1863	Evaluate the Integral	integral from 0 to square root of 3 of (4x)/( square root of x^2+1) with respect to x	$\int_{0}^{\sqrt{3}} \frac{4 x}{\sqrt{x^{2} + 1}} d x$
1864	Evaluate the Integral	integral from 0 to 1 of x^2+ square root of x with respect to x	$\int_{0}^{1} x^{2} + \sqrt{x} d x$
1865	Evaluate the Integral	integral of xe^(5x) with respect to x	$\int x e^{5 x} d x$
1866	Evaluate the Integral	integral of x log of x with respect to x	$\int x \log (x) d x$
1867	Evaluate the Integral	integral of 9thetacos(theta) with respect to theta	$\int 9 θ \cos (θ) d θ$
1868	Evaluate the Integral	integral of xtan(x) with respect to x	$\int x \tan (x) d x$
1869	Evaluate the Integral	integral of sec(3x)tan(3x) with respect to x	$\int \sec (3 x) \tan (3 x) d x$
1870	Evaluate the Integral	integral of sec(4x)tan(4x) with respect to x	$\int \sec (4 x) \tan (4 x) d x$
1871	Evaluate the Integral	integral of sin(8x) with respect to x	$\int \sin (8 x) d x$
1872	Evaluate the Integral	integral of natural log of 4x+1 with respect to x	$\int \ln (4 x + 1) d x$
1873	Evaluate the Integral	integral of sin(pix) with respect to x	$\int \sin (π x) d x$
1874	Evaluate the Integral	integral from 1 to 5 of w^2 natural log of w with respect to w	$\int_{1}^{5} w^{2} \ln (w) d w$
1875	Evaluate the Integral	integral of e^u with respect to u	$\int e^{u} d u$
1876	Evaluate the Integral	integral of 4x^2 with respect to x	$\int 4 x^{2} d x$
1877	Evaluate the Integral	integral of 9z square root of 3z^2-7 with respect to z	$\int 9 z \sqrt{3 z^{2} - 7} d z$
1878	Evaluate the Integral	integral of 1/(x^2 square root of 4-x^2) with respect to x	$\int \frac{1}{x^{2} \sqrt{4 - x^{2}}} d x$
1879	Evaluate the Integral	integral of 2cos(x) with respect to x	$\int 2 \cos (x) d x$
1880	Evaluate the Integral	integral of arctan(8t) with respect to t	$\int \arctan (8 t) d t$
1881	Evaluate the Integral	integral of 3sin(x) with respect to x	$\int 3 \sin (x) d x$
1882	Evaluate the Integral	integral of xe^(x/2) with respect to x	$\int x e^{\frac{x}{2}} d x$
1883	Evaluate the Integral	integral from 0 to 3 of square root of 17 with respect to x	$\int_{0}^{3} \sqrt{17} d x$
1884	Evaluate the Integral	integral of x^3cos(x) with respect to x	$\int x^{3} \cos (x) d x$
1885	Evaluate the Integral	integral of x^(-3/2) with respect to x	$\int x^{- \frac{3}{2}} d x$
1886	Evaluate the Integral	integral of ( natural log of 8x)/x with respect to x	$\int \frac{\ln (8 x)}{x} d x$
1887	Evaluate the Integral	integral of e^(cos(x))sin(x) with respect to x	$\int e^{\cos (x)} \sin (x) d x$
1888	Evaluate the Integral	integral of natural log of cube root of x with respect to x	$\int \ln (\sqrt[3]{x}) d x$
1889	Evaluate the Integral	8 integral from 0 to 1 of x^3 square root of 1-x^2 with respect to x	$8 \int_{0}^{1} x^{3} \sqrt{1 - x^{2}} d x$
1890	Evaluate the Integral	integral of (5x+2)/(2x^2+7x-4) with respect to x	$\int \frac{5 x + 2}{2 x^{2} + 7 x - 4} d x$
1891	Evaluate the Integral	integral from pi/4 to pi of sin(x) with respect to x	$\int_{\frac{π}{4}}^{π} \sin (x) d x$
1892	Evaluate the Integral	integral of 1/( square root of 1-4x^2) with respect to x	$\int \frac{1}{\sqrt{1 - 4 x^{2}}} d x$
1893	Evaluate the Integral	integral of 12/( square root of x) with respect to x	$\int \frac{12}{\sqrt{x}} d x$
1894	Evaluate the Integral	integral of (cos(1/x))/(x^2) with respect to x	$\int \frac{\cos (\frac{1}{x})}{x^{2}} d x$
1895	Evaluate the Integral	integral of (cos( natural log of x))/x with respect to x	$\int \frac{\cos (\ln (x))}{x} d x$
1896	Evaluate the Integral	integral of (t^3)/( square root of 1-t^8) with respect to t	$\int \frac{t^{3}}{\sqrt{1 - t^{8}}} d t$
1897	Evaluate the Integral	integral of (2x-1) natural log of 7x with respect to x	$\int (2 x - 1) \ln (7 x) d x$
1898	Evaluate the Integral	integral of (x^2)/2 with respect to x	$\int \frac{x^{2}}{2} d x$
1899	Evaluate the Integral	integral of (5x^5+5x^2+10)/(x^3-x) with respect to x	$\int \frac{5 x^{5} + 5 x^{2} + 10}{x^{3} - x} d x$
1900	Evaluate the Integral	integral of (x^2+8x)cos(x) with respect to x	$\int (x^{2} + 8 x) \cos (x) d x$