Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
28201	Evaluate the Integral	integral of (x^3-4x^2)/( square root of x) with respect to x	$\int \frac{x^{3} - 4 x^{2}}{\sqrt{x}} d x$
28202	Evaluate the Integral	integral of (x^3-6x+5)/x with respect to x	$\int \frac{x^{3} - 6 x + 5}{x} d x$
28203	Evaluate the Integral	integral of (x^3-6x-20)/(x+5) with respect to x	$\int \frac{x^{3} - 6 x - 20}{x + 5} d x$
28204	Evaluate the Integral	integral of (x^4-1)/(x^2+1) with respect to x	$\int \frac{x^{4} - 1}{x^{2} + 1} d x$
28205	Evaluate the Integral	integral of (x^4-4x^3-x-6)/(x^3-4x^2) with respect to x	$\int \frac{x^{4} - 4 x^{3} - x - 6}{x^{3} - 4 x^{2}} d x$
28206	Evaluate the Integral	integral of (x^5e^x-2x^4)/(x^5) with respect to x	$\int \frac{x^{5} e^{x} - 2 x^{4}}{x^{5}} d x$
28207	Evaluate the Integral	integral of (x^5)/((4-x^6)^2) with respect to x	$\int \frac{x^{5}}{{(4 - x^{6})}^{2}} d x$
28208	Evaluate the Integral	integral of (x^5)/(1+x^12) with respect to x	$\int \frac{x^{5}}{1 + x^{12}} d x$
28209	Evaluate the Integral	integral of (x^5+2x^2-1)/(x^4) with respect to x	$\int \frac{x^{5} + 2 x^{2} - 1}{x^{4}} d x$
28210	Evaluate the Integral	integral of (x^5+7)/(x^2) with respect to x	$\int \frac{x^{5} + 7}{x^{2}} d x$
28211	Find the Inflection Points	natural log of x^2+4	$\ln (x^{2} + 4)$
28212	Evaluate the Integral	integral of 1/((x^2-1)^(3/2)) with respect to x	$\int \frac{1}{{(x^{2} - 1)}^{\frac{3}{2}}} d x$
28213	Evaluate the Integral	integral of 1/((x-1) square root of 4x^2-8x+3) with respect to x	$\int \frac{1}{(x - 1) \sqrt{4 x^{2} - 8 x + 3}} d x$
28214	Evaluate the Integral	integral of 1/((x-1)(x+3)) with respect to x	$\int \frac{1}{(x - 1) (x + 3)} d x$
28215	Evaluate the Integral	integral of 1/((36+x^2)^2) with respect to x	$\int \frac{1}{{(36 + x^{2})}^{2}} d x$
28216	Evaluate the Integral	integral of 1/((2x-1)^3) with respect to x	$\int \frac{1}{{(2 x - 1)}^{3}} d x$
28217	Evaluate the Integral	integral of 1/((x^2-4)^(3/2)) with respect to x	$\int \frac{1}{{(x^{2} - 4)}^{\frac{3}{2}}} d x$
28218	Evaluate the Integral	integral of 1/((x^2-6x+13)^(3/2)) with respect to x	$\int \frac{1}{{(x^{2} - 6 x + 13)}^{\frac{3}{2}}} d x$
28219	Evaluate the Integral	integral of 1/((x^2-8x+29)^(3/2)) with respect to x	$\int \frac{1}{{(x^{2} - 8 x + 29)}^{\frac{3}{2}}} d x$
28220	Evaluate the Integral	integral of 1/((z^2-2z+5)^2) with respect to x	$\int \frac{1}{{(z^{2} - 2 z + 5)}^{2}} d x$
28221	Evaluate the Integral	integral of 1/(1-r^2) with respect to r	$\int \frac{1}{1 - r^{2}} d r$
28222	Evaluate the Integral	integral of 1.1/(r natural log of r) with respect to r	$\int \frac{1.1}{r \ln (r)} d r$
28223	Evaluate the Integral	integral of (x^9-1)/(x^5) with respect to x	$\int \frac{x^{9} - 1}{x^{5}} d x$
28224	Evaluate the Integral	integral of (x^7e^x-6x^6)/(x^7) with respect to x	$\int \frac{x^{7} e^{x} - 6 x^{6}}{x^{7}} d x$
28225	Evaluate the Integral	integral of (x^5-2x)/(x^4) with respect to x	$\int \frac{x^{5} - 2 x}{x^{4}} d x$
28226	Evaluate the Integral	integral of (x^8)/(x^9-8) with respect to x	$\int \frac{x^{8}}{x^{9} - 8} d x$
28227	Evaluate the Integral	integral of (y^2)/4 with respect to y	$\int \frac{y^{2}}{4} d y$
28228	Evaluate the Integral	integral of \|1-x\| with respect to x	$\int \| 1 - x \| d x$
28229	Evaluate the Integral	integral of (z^2)/(z^3+1) with respect to z	$\int \frac{z^{2}}{z^{3} + 1} d z$
28230	Evaluate the Integral	integral of (y^2)/((y^3+5)^2) with respect to y	$\int \frac{y^{2}}{{(y^{3} + 5)}^{2}} d y$
28231	Evaluate the Integral	integral of (y^3)/((1+2y^4)^5) with respect to y	$\int \frac{y^{3}}{{(1 + 2 y^{4})}^{5}} d y$
28232	Evaluate the Integral	integral of (x^2-25)/(x-5) with respect to x	$\int \frac{x^{2} - 25}{x - 5} d x$
28233	Evaluate the Integral	integral of (x^2-3)/(x^3-9x+3) with respect to x	$\int \frac{x^{2} - 3}{x^{3} - 9 x + 3} d x$
28234	Evaluate the Integral	integral of (x^2-32)/x with respect to x	$\int \frac{x^{2} - 32}{x} d x$
28235	Evaluate the Integral	integral of (x^2-34)/x with respect to x	$\int \frac{x^{2} - 34}{x} d x$
28236	Evaluate the Integral	integral of (x^2-3x)/(x^2-3x-28) with respect to x	$\int \frac{x^{2} - 3 x}{x^{2} - 3 x - 28} d x$
28237	Evaluate the Integral	integral of (x^2-14x+10)/(x+12) with respect to x	$\int \frac{x^{2} - 14 x + 10}{x + 12} d x$
28238	Evaluate the Integral	integral of (x^2+2x-1)/(2x^3+3x^2-2x) with respect to x	$\int \frac{x^{2} + 2 x - 1}{2 x^{3} + 3 x^{2} - 2 x} d x$
28239	Evaluate the Integral	integral of (x^2+6x+4)/(x^4+8x^2+16) with respect to x	$\int \frac{x^{2} + 6 x + 4}{x^{4} + 8 x^{2} + 16} d x$
28240	Evaluate the Integral	integral of (x^2+8x-3)/(x^3+3x^2) with respect to x	$\int \frac{x^{2} + 8 x - 3}{x^{3} + 3 x^{2}} d x$
28241	Evaluate the Integral	integral of (x^2)/( square root of 64-x^2) with respect to x	$\int \frac{x^{2}}{\sqrt{64 - x^{2}}} d x$
28242	Evaluate the Integral	integral of (x^2+1)/((x-10)(x-9)^2) with respect to x	$\int \frac{x^{2} + 1}{(x - 10) {(x - 9)}^{2}} d x$
28243	Evaluate the Integral	integral of (sec(1/(x^7))^2)/(x^8) with respect to x	$\int \frac{\sec^{2} (\frac{1}{x^{7}})}{x^{8}} d x$
28244	Evaluate the Integral	integral of sin(x)^2(x)cos(x)^3(x) with respect to x	$\int \sin^{2} (x) (x) \cos^{3} (x) (x) d x$
28245	Evaluate the Integral	integral of (sec(1-t)^4)/(tan(1-t)^8) with respect to t	$\int \frac{\sec^{4} (1 - t)}{\tan^{8} (1 - t)} d t$
28246	Evaluate the Integral	integral of (t^3)/( cube root of 4+t^4) with respect to t	$\int \frac{t^{3}}{\sqrt[3]{4 + t^{4}}} d t$
28247	Evaluate the Integral	integral of (t^2+3)/(t^2+1) with respect to t	$\int \frac{t^{2} + 3}{t^{2} + 1} d t$
28248	Evaluate the Integral	integral of (arctan(5x))/(1+25x^2) with respect to x	$\int \frac{\arctan (5 x)}{1 + 25 x^{2}} d x$
28249	Evaluate the Integral	integral of (t^3+ cube root of t)/(t^2) with respect to t	$\int \frac{t^{3} + \sqrt[3]{t}}{t^{2}} d t$
28250	Evaluate the Integral	integral of (t^6+4)/(t^6) with respect to t	$\int \frac{t^{6} + 4}{t^{6}} d t$
28251	Evaluate the Integral	integral of ( square root of x^2+64)/(2x^2) with respect to x	$\int \frac{\sqrt{x^{2} + 64}}{2 x^{2}} d x$
28252	Evaluate the Integral	integral of ( square root of x^2-81)/(x^3) with respect to x	$\int \frac{\sqrt{x^{2} - 81}}{x^{3}} d x$
28253	Evaluate the Integral	integral of ( square root of x^2-16)/x with respect to x	$\int \frac{\sqrt{x^{2} - 16}}{x} d x$
28254	Evaluate the Integral	integral of (arctan(9x))/(1+81x^2) with respect to x	$\int \frac{\arctan (9 x)}{1 + 81 x^{2}} d x$
28255	Evaluate the Integral	integral of (u^9-6u^7+12)/(u^7) with respect to u	$\int \frac{u^{9} - 6 u^{7} + 12}{u^{7}} d u$
28256	Evaluate the Integral	integral of (u^7-3u^4+8)/(u^4) with respect to u	$\int \frac{u^{7} - 3 u^{4} + 8}{u^{4}} d u$
28257	Evaluate the Integral	integral of (u^5+1)/(u^2) with respect to u	$\int \frac{u^{5} + 1}{u^{2}} d u$
28258	Evaluate the Integral	integral of ( square root of cos(2x))/(sin(x)) with respect to x	$\int \frac{\sqrt{\cos (2 x)}}{\sin (x)} d x$
28259	Evaluate the Integral	integral of ( square root of 2)/(3t^2+3) with respect to t	$\int \frac{\sqrt{2}}{3 t^{2} + 3} d t$
28260	Find dy/dx at (-1,1)	(2x+2y)^3=8x^3+8y^3 , (-1,1)	${(2 x + 2 y)}^{3} = 8 x^{3} + 8 y^{3}$ , $(- 1, 1)$
28261	Evaluate the Integral	integral of ( cube root of 8+ square root of x)/( square root of x) with respect to x	$\int \frac{\sqrt[3]{8 + \sqrt{x}}}{\sqrt{x}} d x$
28262	Evaluate the Integral	integral of (x^2e^x-2x)/(x^2) with respect to x	$\int \frac{x^{2} e^{x} - 2 x}{x^{2}} d x$
28263	Evaluate the Integral	integral of 1/( square root of 6x+1) with respect to x	$\int \frac{1}{\sqrt{6 x + 1}} d x$
28264	Evaluate the Integral	integral of 1/( square root of 7x) with respect to x	$\int \frac{1}{\sqrt{7 x}} d x$
28265	Evaluate the Integral	integral of 1/( square root of tan(x)) with respect to x	$\int \frac{1}{\sqrt{\tan (x)}} d x$
28266	Evaluate	1/2*e^10-1/2	$\frac{1}{2} \cdot e^{10} - \frac{1}{2}$
28267	Evaluate	sin(4pi)	$\sin (4 π)$
28268	Evaluate the Integral	integral of 1/( square root of 3-4x^2) with respect to x	$\int \frac{1}{\sqrt{3 - 4 x^{2}}} d x$
28269	Evaluate the Integral	integral of 1/( square root of 36-x^2) with respect to x	$\int \frac{1}{\sqrt{36 - x^{2}}} d x$
28270	Evaluate the Integral	integral of 1/( square root of 1-8x^2) with respect to x	$\int \frac{1}{\sqrt{1 - 8 x^{2}}} d x$
28271	Evaluate the Integral	integral from 0 to pi/6 of x^2cos(3x) with respect to x	$\int_{0}^{\frac{π}{6}} x^{2} \cos (3 x) d x$
28272	Evaluate the Integral	integral of 1/( square root of 5s+4) with respect to s	$\int \frac{1}{\sqrt{5 s + 4}} d s$
28273	Evaluate the Integral	integral of 1/( square root of 5x^2+1) with respect to x	$\int \frac{1}{\sqrt{5 x^{2} + 1}} d x$
28274	Evaluate the Integral	integral of 1/( square root of 4x^2-25) with respect to x	$\int \frac{1}{\sqrt{4 x^{2} - 25}} d x$
28275	Evaluate the Integral	integral of 1/( square root of 4s+3) with respect to s	$\int \frac{1}{\sqrt{4 s + 3}} d s$
28276	Evaluate the Integral	integral of 1/(u^2+1) with respect to x	$\int \frac{1}{u^{2} + 1} d x$
28277	Evaluate the Integral	integral of 1/( square root of x^2-49) with respect to x	$\int \frac{1}{\sqrt{x^{2} - 49}} d x$
28278	Evaluate the Integral	integral of 1/(s^2(s-1)^2) with respect to s	$\int \frac{1}{s^{2} {(s - 1)}^{2}} d s$
28279	Evaluate the Integral	integral of 1/(sec(y)^2) with respect to y	$\int \frac{1}{\sec^{2} (y)} d y$
28280	Evaluate the Integral	integral of 1/(t^3 square root of t^2-9) with respect to t	$\int \frac{1}{t^{3} \sqrt{t^{2} - 9}} d t$
28281	Evaluate the Integral	integral of 1/(tan(x)^2) with respect to x	$\int \frac{1}{\tan^{2} (x)} d x$
28282	Evaluate the Integral	integral of 1/(v(x-2)) with respect to x	$\int \frac{1}{v (x - 2)} d x$
28283	Evaluate the Integral	integral of 1/(e^(2x)+e^(-2x)) with respect to x	$\int \frac{1}{e^{2 x} + e^{- 2 x}} d x$
28284	Evaluate the Integral	integral of 1/(ax^(2+b)) with respect to x	$\int \frac{1}{a x^{2 + b}} d x$
28285	Evaluate the Integral	integral of 1/(cos(t)^2 ninth root of 8+tan(t)) with respect to t	$\int \frac{1}{\cos^{2} (t) \sqrt[9]{8 + \tan (t)}} d t$
28286	Evaluate the Integral	integral of 1/(cos(x)^4) with respect to x	$\int \frac{1}{\cos^{4} (x)} d x$
28287	Evaluate the Integral	integral of 1/(x^2)*sin(1/x) with respect to x	$\int \frac{1}{x^{2}} \cdot \sin (\frac{1}{x}) d x$
28288	Evaluate the Integral	integral of 1/(x^2-5x+6) with respect to x	$\int \frac{1}{x^{2} - 5 x + 6} d x$
28289	Evaluate the Integral	integral of 1/(x^2-6x+9) with respect to x	$\int \frac{1}{x^{2} - 6 x + 9} d x$
28290	Evaluate the Integral	integral of 1/(x^2-7x+10) with respect to x	$\int \frac{1}{x^{2} - 7 x + 10} d x$
28291	Evaluate the Integral	integral of 1/(x^2-2x-3) with respect to x	$\int \frac{1}{x^{2} - 2 x - 3} d x$
28292	Evaluate the Integral	integral of 1/(x^2+5x+4) with respect to x	$\int \frac{1}{x^{2} + 5 x + 4} d x$
28293	Evaluate the Integral	integral of 1/(x^2+36) with respect to x	$\int \frac{1}{x^{2} + 36} d x$
28294	Evaluate the Integral	integral of 1/(x^(2/3)(1+x^(1/3))) with respect to x	$\int \frac{1}{x^{\frac{2}{3}} (1 + x^{\frac{1}{3}})} d x$
28295	Evaluate the Integral	integral of 1/(x^2 square root of x^2-49) with respect to x	$\int \frac{1}{x^{2} \sqrt{x^{2} - 49}} d x$
28296	Evaluate the Integral	integral of 1/(x^2-y^2) with respect to x	$\int \frac{1}{x^{2} - y^{2}} d x$
28297	Evaluate the Integral	integral of 1/(v^2) with respect to v	$\int \frac{1}{v^{2}} d v$
28298	Evaluate the Integral	integral of 1/( cube root of x^2) with respect to x	$\int \frac{1}{\sqrt[3]{x^{2}}} d x$
28299	Evaluate the Integral	integral of 1/( fifth root of x^6) with respect to x	$\int \frac{1}{\sqrt[5]{x^{6}}} d x$
28300	Evaluate the Integral	integral of 1/( fourth root of 1+x) with respect to x	$\int \frac{1}{\sqrt[4]{1 + x}} d x$