Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
2201	Evaluate the Integral	integral of 1/(x^7) with respect to x	$\int \frac{1}{x^{7}} d x$
2202	Evaluate the Integral	integral of 1/( square root of x^2-9) with respect to x	$\int \frac{1}{\sqrt{x^{2} - 9}} d x$
2203	Evaluate the Integral	integral of ( square root of x^2-4)/x with respect to x	$\int \frac{\sqrt{x^{2} - 4}}{x} d x$
2204	Evaluate the Integral	integral of (x^2+2x-3)/(x^4) with respect to x	$\int \frac{x^{2} + 2 x - 3}{x^{4}} d x$
2205	Evaluate the Integral	integral of (5-x)/(2x^2+x-1) with respect to x	$\int \frac{5 - x}{2 x^{2} + x - 1} d x$
2206	Evaluate the Integral	integral of a^x with respect to x	$\int a^{x} d x$
2207	Evaluate the Integral	integral of (arcsin(x))/( square root of 1-x^2) with respect to x	$\int \frac{\arcsin (x)}{\sqrt{1 - x^{2}}} d x$
2208	Evaluate the Integral	integral of (2x)/(x^2+1) with respect to x	$\int \frac{2 x}{x^{2} + 1} d x$
2209	Evaluate the Integral	integral of sin(3x)^2 with respect to x	$\int \sin^{2} (3 x) d x$
2210	Evaluate the Integral	integral of sec(x)^3tan(x)^3 with respect to x	$\int \sec^{3} (x) \tan^{3} (x) d x$
2211	Evaluate the Integral	integral of (sin(1/x))/(x^2) with respect to x	$\int \frac{\sin (\frac{1}{x})}{x^{2}} d x$
2212	Evaluate the Integral	integral of square root of 1-4y with respect to y	$\int \sqrt{1 - 4 y} d y$
2213	Evaluate the Integral	integral of square root of x^9 with respect to x	$\int \sqrt{x^{9}} d x$
2214	Evaluate the Integral	integral of sin(x)^3cos(x)^4 with respect to x	$\int \sin^{3} (x) \cos^{4} (x) d x$
2215	Evaluate the Integral	integral of e^(11x) with respect to x	$\int e^{11 x} d x$
2216	Evaluate the Integral	integral of e^xcos(e^x) with respect to x	$\int e^{x} \cos (e^{x}) d x$
2217	Evaluate the Integral	integral of e^(-x)cos(2x) with respect to x	$\int e^{- x} \cos (2 x) d x$
2218	Evaluate the Integral	integral of e^(3x)cos(2x) with respect to x	$\int e^{3 x} \cos (2 x) d x$
2219	Evaluate the Integral	integral of x^11 with respect to x	$\int x^{11} d x$
2220	Evaluate the Integral	integral of x/(x^2+2x+2) with respect to x	$\int \frac{x}{x^{2} + 2 x + 2} d x$
2221	Evaluate the Integral	integral of x/(x^2+4) with respect to x	$\int \frac{x}{x^{2} + 4} d x$
2222	Evaluate the Integral	integral of x^2(x^3+5)^9 with respect to x	$\int x^{2} {(x^{3} + 5)}^{9} d x$
2223	Evaluate the Integral	integral of x^2e^(5x) with respect to x	$\int x^{2} e^{5 x} d x$
2224	Evaluate the Integral	integral of x^2e^(-3x) with respect to x	$\int x^{2} e^{- 3 x} d x$
2225	Evaluate the Integral	integral of x^2sec(x^3)^2 with respect to x	$\int x^{2} \sec^{2} (x^{3}) d x$
2226	Evaluate the Integral	integral of fourth root of x^3 with respect to x	$\int \sqrt[4]{x^{3}} d x$
2227	Evaluate the Integral	integral of cube root of x^8 with respect to x	$\int \sqrt[3]{x^{8}} d x$
2228	Evaluate the Integral	integral of fifth root of x^2 with respect to x	$\int \sqrt[5]{x^{2}} d x$
2229	Evaluate the Integral	integral of fifth root of x with respect to x	$\int \sqrt[5]{x} d x$
2230	Evaluate the Integral	integral of x^2sin(3x) with respect to x	$\int x^{2} \sin (3 x) d x$
2231	Evaluate the Integral	integral of x^9e^(x^10) with respect to x	$\int x^{9} e^{x^{10}} d x$
2232	Evaluate the Integral	integral of y^2 square root of y with respect to y	$\int y^{2} \sqrt{y} d y$
2233	Evaluate the Integral	integral from -3 to 4 of \|x\| with respect to x	$\int_{- 3}^{4} \| x \| d x$
2234	Evaluate the Integral	integral of 3t with respect to t	$\int 3 t d t$
2235	Evaluate the Integral	integral of 30x^(3/2) with respect to x	$\int 30 x^{\frac{3}{2}} d x$
2236	Evaluate the Integral	integral from -4 to 2 of 2x+4 with respect to x	$\int_{- 4}^{2} 2 x + 4 d x$
2237	Evaluate the Integral	integral from -4 to 4 of 16-x^2 with respect to x	$\int_{- 4}^{4} 16 - x^{2} d x$
2238	Evaluate the Integral	integral of 2cos(2x) with respect to x	$\int 2 \cos (2 x) d x$
2239	Evaluate the Integral	integral from 7 to 2 of g(x) with respect to x	$\int_{7}^{2} g (x) d x$
2240	Evaluate the Integral	integral of 6x-5 with respect to x	$\int 6 x - 5 d x$
2241	Evaluate the Integral	integral of 6 with respect to k	$\int 6 d k$
2242	Evaluate the Integral	integral of 6e^(-7x) with respect to x	$\int 6 e^{- 7 x} d x$
2243	Evaluate the Integral	integral of 6x^(1/2) with respect to x	$\int 6 x^{\frac{1}{2}} d x$
2244	Evaluate the Integral	integral of 8e^(4x) with respect to x	$\int 8 e^{4 x} d x$
2245	Evaluate the Integral	integral of 5x^-1 with respect to x	$\int 5 x^{- 1} d x$
2246	Evaluate the Integral	integral of 4e^(2x) with respect to x	$\int 4 e^{2 x} d x$
2247	Evaluate the Integral	integral of 4e^(4x) with respect to x	$\int 4 e^{4 x} d x$
2248	Evaluate the Integral	integral of 5(t^2-5t-2) with respect to t	$\int 5 (t^{2} - 5 t - 2) d t$
2249	Find the Derivative - d/dI	natural log of infinity	$\ln (\infty)$
2250	Find the Derivative - d/dx	4	$4$
2251	Evaluate the Integral	integral of natural log of 4x with respect to x	$\int \ln (4 x) d x$
2252	Evaluate the Integral	integral of natural log of 7x with respect to x	$\int \ln (7 x) d x$
2253	Evaluate the Integral	integral of sin(4x)cos(4x) with respect to x	$\int \sin (4 x) \cos (4 x) d x$
2254	Evaluate the Integral	integral of sin(y) with respect to y	$\int \sin (y) d y$
2255	Evaluate the Integral	integral of sec(4x) with respect to x	$\int \sec (4 x) d x$
2256	Evaluate the Integral	integral of sec(3x) with respect to x	$\int \sec (3 x) d x$
2257	Evaluate the Integral	integral of sec(x)(sec(x)+tan(x)) with respect to x	$\int \sec (x) (\sec (x) + \tan (x)) d x$
2258	Evaluate the Integral	integral of x natural log of 2x with respect to x	$\int x \ln (2 x) d x$
2259	Evaluate the Integral	integral of x(x^2-1)^4 with respect to x	$\int x {(x^{2} - 1)}^{4} d x$
2260	Evaluate the Integral	integral of xtan(x)^2 with respect to x	$\int x \tan^{2} (x) d x$
2261	Evaluate the Integral	integral from 0 to 1 of e^(-x) with respect to x	$\int_{0}^{1} e^{- x} d x$
2262	Evaluate the Integral	integral from 0 to 1 of square root of 1-x^2 with respect to x	$\int_{0}^{1} \sqrt{1 - x^{2}} d x$
2263	Evaluate the Integral	integral from 0 to 1 of (u+2)(u-3) with respect to u	$\int_{0}^{1} (u + 2) (u - 3) d u$
2264	Evaluate the Integral	integral from 0 to 11 of square root of 121-x^2 with respect to x	$\int_{0}^{11} \sqrt{121 - x^{2}} d x$
2265	Evaluate the Integral	integral from 0 to 6 of x/( square root of 9+2x^2) with respect to x	$\int_{0}^{6} \frac{x}{\sqrt{9 + 2 x^{2}}} d x$
2266	Evaluate the Integral	integral from 0 to 2 of 8x^2 with respect to x	$\int_{0}^{2} 8 x^{2} d x$
2267	Evaluate the Integral	integral from 1 to 2 of 2u^2+3 with respect to u udu	$\int_{1}^{2} 2 u^{2} + 3 d u$ udu
2268	Evaluate the Integral	integral from 1 to 2 of (t+1/t)^2 with respect to x	$\int_{1}^{2} {(t + \frac{1}{t})}^{2} d x$
2269	Evaluate the Integral	integral from 1 to 3 of x^2 natural log of x with respect to x	$\int_{1}^{3} x^{2} \ln (x) d x$
2270	Evaluate the Integral	integral from 1 to 3 of 1/x with respect to x	$\int_{1}^{3} \frac{1}{x} d x$
2271	Evaluate the Integral	integral from 1 to 3 of x^2 with respect to x	$\int_{1}^{3} x^{2} d x$
2272	Evaluate the Integral	integral from 2 to 3 of 1/( square root of x)-7 with respect to x	$\int_{2}^{3} \frac{1}{\sqrt{x}} - 7 d x$
2273	Evaluate the Integral	integral from -2 to 2 of \|x\| with respect to x	$\int_{- 2}^{2} \| x \| d x$
2274	Evaluate the Integral	integral from -2 to 3 of 36-x^2 with respect to x	$\int_{- 2}^{3} 36 - x^{2} d x$
2275	Evaluate the Integral	integral of 15x^(1/2) with respect to x	$\int 15 x^{\frac{1}{2}} d x$
2276	Evaluate the Integral	integral of 15x^(3/2) with respect to x	$\int 15 x^{\frac{3}{2}} d x$
2277	Evaluate the Integral	integral of 16x with respect to x	$\int 16 x d x$
2278	Evaluate the Integral	integral of 11x^-6 with respect to x	$\int 11 x^{- 6} d x$
2279	Evaluate the Integral	integral from 10 to 13 of 2x with respect to x	$\int_{10}^{13} 2 x d x$
2280	Evaluate the Integral	integral from 1 to 8 of 1/x with respect to x	$\int_{1}^{8} \frac{1}{x} d x$
2281	Evaluate the Integral	integral from 1 to 8 of ( natural log of x)/x with respect to x	$\int_{1}^{8} \frac{\ln (x)}{x} d x$
2282	Evaluate the Integral	integral from 1 to 6 of x square root of 5x^2+4 with respect to x	$\int_{1}^{6} x \sqrt{5 x^{2} + 4} d x$
2283	Evaluate	(8/27)^(-1/3)(81/256)^(-1/4)	${(\frac{8}{27})}^{- \frac{1}{3}} {(\frac{81}{256})}^{- \frac{1}{4}}$
2284	Find the Derivative of the Integral	integral of square root of x with respect to x	$\int \sqrt{x} d x$
2285	Find the Derivative - d/dx	1/3x^3	$\frac{1}{3} x^{3}$
2286	Find the Derivative of the Integral	integral of tan(x) with respect to x	$\int \tan (x) d x$
2287	Find the Derivative of the Integral	integral of xcos(x) with respect to x	$\int x \cos (x) d x$
2288	Find the Derivative - d/dx	3x^2-4x	$3 x^{2} - 4 x$
2289	Find the 3rd Derivative	y=1/x	$y = \frac{1}{x}$
2290	Find the Derivative - d/dx	x/12-12/x	$\frac{x}{12} - \frac{12}{x}$
2291	Find dy/dx	(x^2+y^2)^2=4x^2y	${(x^{2} + y^{2})}^{2} = 4 x^{2} y$
2292	Find the Derivative - d/d@VAR	f(x)=e^(-x) square root of x	$f (x) = e^{- x} \sqrt{x}$
2293	Evaluate the Integral	integral from 1 to 2 of (e^(1/x))/(x^2) with respect to x	$\int_{1}^{2} \frac{e^{\frac{1}{x}}}{x^{2}} d x$
2294	Find the Average Value of the Derivative	y=25-x^2 , [-5,5]	$y = 25 - x^{2}$ , $[- 5, 5]$
2295	Find the Concavity	f(x)=1/2x^4+2x^3	$f (x) = \frac{1}{2} x^{4} + 2 x^{3}$
2296	Find the Inflection Points	y=x^3-6x^2-36x	$y = x^{3} - 6 x^{2} - 36 x$
2297	Find the Critical Points	x+1/x	$x + \frac{1}{x}$
2298	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3+3x^2-24x+6	$f (x) = x^{3} + 3 x^{2} - 24 x + 6$
2299	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^3+3x^2-72x	$f (x) = 2 x^{3} + 3 x^{2} - 72 x$
2300	Find the Horizontal Tangent Line	x^2+y^2=-14x	$x^{2} + y^{2} = - 14 x$