Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
27201	Evaluate the Integral	integral of (10x-3)^2 with respect to x	$\int {(10 x - 3)}^{2} d x$
27202	Find the Derivative - d/dx	(2x-1)/(2x+1)	$\frac{2 x - 1}{2 x + 1}$
27203	Find the Derivative - d/dx	(x^2+28)^(4/5)	${(x^{2} + 28)}^{\frac{4}{5}}$
27204	Evaluate the Integral	integral of (e^t+1)/(e^t+t) with respect to t	$\int \frac{e^{t} + 1}{e^{t} + t} d t$
27205	Evaluate the Integral	integral of (x+5)e^((x+5)^2) with respect to x	$\int (x + 5) e^{{(x + 5)}^{2}} d x$
27206	Evaluate the Integral	integral from -0.4772 to 0.4987 of x with respect to x	$\int_{- 0.4772}^{0.4987} x d x$
27207	Evaluate	sec(-pi/4)	$\sec (- \frac{π}{4})$
27208	Evaluate the Integral	integral of ((2x-1)^2)/2 with respect to x	$\int \frac{{(2 x - 1)}^{2}}{2} d x$
27209	Evaluate the Integral	integral of (x+2)/(x^2+2x+10) with respect to x	$\int \frac{x + 2}{x^{2} + 2 x + 10} d x$
27210	Evaluate the Summation	sum from k=1 to 900 of 4k+6	$\sum_{k = 1}^{900} 4 k + 6$
27211	Evaluate the Integral	integral of (2^( natural log of x))/x with respect to x	$\int \frac{2^{\ln (x)}}{x} d x$
27212	Evaluate the Integral	integral of (5^x)/( natural log of 5) with respect to x	$\int \frac{5^{x}}{\ln (5)} d x$
27213	Evaluate the Summation	sum from n=1 to 4 of (1/6)^(n-1)	$\sum_{n = 1}^{4} {(\frac{1}{6})}^{n - 1}$
27214	Evaluate the Integral	integral of (3x-2)^20 with respect to x	$\int {(3 x - 2)}^{20} d x$
27215	Evaluate the Integral	integral of (3x-4)^2 with respect to x	$\int {(3 x - 4)}^{2} d x$
27216	Evaluate the Integral	integral of (4x-2)/(x^3-x^2-2x) with respect to x	$\int \frac{4 x - 2}{x^{3} - x^{2} - 2 x} d x$
27217	Evaluate the Integral	integral of (4x^3+16x)^3(3x^2+4) with respect to x	$\int {(4 x^{3} + 16 x)}^{3} (3 x^{2} + 4) d x$
27218	Evaluate the Integral	integral of (36-9x^2)^(-3/2) with respect to x	$\int {(36 - 9 x^{2})}^{- \frac{3}{2}} d x$
27219	Evaluate the Integral	integral of (3-8x)^5 with respect to x	$\int {(3 - 8 x)}^{5} d x$
27220	Evaluate the Integral	integral of (4x^2-16x+7)^4(x-2) with respect to x	$\int {(4 x^{2} - 16 x + 7)}^{4} (x - 2) d x$
27221	Evaluate the Integral	integral of (5x-3)^4 with respect to x	$\int {(5 x - 3)}^{4} d x$
27222	Evaluate the Integral	integral of (5x-7)/(x^2-3x+2) with respect to x	$\int \frac{5 x - 7}{x^{2} - 3 x + 2} d x$
27223	Evaluate the Integral	integral of (5+11x^2)^2 with respect to x	$\int {(5 + 11 x^{2})}^{2} d x$
27224	Evaluate the Integral	integral of (6t^2-2)/(t^3-t) with respect to t	$\int \frac{6 t^{2} - 2}{t^{3} - t} d t$
27225	Evaluate the Integral	integral of ( square root of x^2-16)/(x^3) with respect to x	$\int \frac{\sqrt{x^{2} - 16}}{x^{3}} d x$
27226	Evaluate the Integral	integral of ( square root of 1-x^2)/x with respect to x	$\int \frac{\sqrt{1 - x^{2}}}{x} d x$
27227	Evaluate the Integral	integral of (w^2-w+6)/(w^3+3w) with respect to w	$\int \frac{w^{2} - w + 6}{w^{3} + 3 w} d w$
27228	Evaluate the Integral	integral of (u^7-2u^4+6)/(u^4) with respect to u	$\int \frac{u^{7} - 2 u^{4} + 6}{u^{4}} d u$
27229	Evaluate the Integral	integral of (e^x)/(e^(2x)) with respect to x	$\int \frac{e^{x}}{e^{2 x}} d x$
27230	Evaluate the Integral	integral from 0 to 12 of square root of 144-x^2 with respect to x	$\int_{0}^{12} \sqrt{144 - x^{2}} d x$
27231	Evaluate the Integral	integral of (e^(2t))/((3-e^(2t))^8) with respect to tdx	$\int \frac{e^{2 t}}{{(3 - e^{2 t})}^{8}} d t d x$
27232	Evaluate the Function	f(x)=( natural log of x)^4 at x=10	$\int \frac{e^{2 x}}{1 + 6 e^{2 x} + 9 e^{4 x}} d x$
27233	Evaluate the Integral	integral of (e^x-5x)/7 with respect to x	$\int \frac{e^{x} - 5 x}{7} d x$
27234	Evaluate the Integral	integral of ( natural log of (x)^15)/x with respect to x	$\int \frac{\ln ({(x)}^{15})}{x} d x$
27235	Evaluate the Integral	integral of ( log base 3 of x)/(x^2) with respect to x	$\int \frac{\log_{3} (x)}{x^{2}} d x$
27236	Evaluate the Integral	integral of (x^3+1)/(x-1) with respect to x	$\int \frac{x^{3} + 1}{x - 1} d x$
27237	Evaluate the Integral	integral of (x^3+8)/(x+2) with respect to x	$\int \frac{x^{3} + 8}{x + 2} d x$
27238	Evaluate the Integral	integral of (x^4)/(1+x) with respect to x	$\int \frac{x^{4}}{1 + x} d x$
27239	Evaluate the Integral	integral of (x^2-x+9)/((x^2+9)^2) with respect to x	$\int \frac{x^{2} - x + 9}{{(x^{2} + 9)}^{2}} d x$
27240	Evaluate the Integral	integral of (x^2+3x-4)/(x^3-4x^2+4x) with respect to x	$\int \frac{x^{2} + 3 x - 4}{x^{3} - 4 x^{2} + 4 x} d x$
27241	Evaluate the Integral	integral of (x^2+3x-4)/(x+2) with respect to x	$\int \frac{x^{2} + 3 x - 4}{x + 2} d x$
27242	Evaluate the Integral	integral of (x^2-4)/(x+2) with respect to x	$\int \frac{x^{2} - 4}{x + 2} d x$
27243	Evaluate the Integral	integral of square root of 16-4x^2 with respect to x	$\int \sqrt{16 - 4 x^{2}} d x$
27244	Evaluate the Integral	integral of (x^3)/((1+x^4)( natural log of 1+x^4)) with respect to x	$\int \frac{x^{3}}{(1 + x^{4}) (\ln (1 + x^{4}))} d x$
27245	Evaluate the Integral	integral of x^2sin(2x) with respect to x	$\int x^{2} \sin (2 x) d x$
27246	Find the Horizontal Tangent Line	y=x^3-12x+2	$y = x^{3} - 12 x + 2$
27247	Find the Critical Points	f(x)=x^2-4x+3	$f (x) = x^{2} - 4 x + 3$
27248	Evaluate the Integral	integral of 1/(x^2-25) with respect to x	$\int \frac{1}{x^{2} - 25} d x$
27249	Evaluate the Integral	integral of 1/(x^2+8x+7) with respect to x	$\int \frac{1}{x^{2} + 8 x + 7} d x$
27250	Find Where Increasing/Decreasing Using Derivatives	x^3+3x^2-24x+6	$x^{3} + 3 x^{2} - 24 x + 6$
27251	Evaluate the Integral	integral of 1/(x^2-10) with respect to x	$\int \frac{1}{x^{2} - 10} d x$
27252	Find Where Increasing/Decreasing Using Derivatives	x^4-18x^2	$x^{4} - 18 x^{2}$
27253	Find the Derivative - d/dt	1/3t^3	$\frac{1}{3} t^{3}$
27254	Find the Derivative - d/dI	cos(infinity)	$\cos (\infty)$
27255	Evaluate the Integral	integral of 1/(x^2)*(sin(1/x)cos(1/x)) with respect to x	$\int \frac{1}{x^{2}} \cdot (\sin (\frac{1}{x}) \cos (\frac{1}{x})) d x$
27256	Evaluate the Integral	integral of 1/(x^2 square root of 16x^2-9) with respect to x	$\int \frac{1}{x^{2} \sqrt{16 x^{2} - 9}} d x$
27257	Evaluate the Integral	integral of 1/(1+25y^2) with respect to x	$\int \frac{1}{1 + 25 y^{2}} d x$
27258	Find the Derivative - d/d@VAR	f(x)=(8x-x^2)^3	$f (x) = {(8 x - x^{2})}^{3}$
27259	Find the Derivative - d/d@VAR	f(x)=(2000x)/(4x+75)	$f (x) = \frac{2000 x}{4 x + 75}$
27260	Evaluate the Integral	integral of 1/(16-x^2) with respect to x	$\int \frac{1}{16 - x^{2}} d x$
27261	Find the Derivative - d/d@VAR	f(x)=1/(9x^2)	$f (x) = \frac{1}{9 x^{2}}$
27262	Find the Derivative - d/d@VAR	f(x) = square root of 10x^2-x	$f (x) = \sqrt{10 x^{2} - x}$
27263	Evaluate the Integral	integral of 1/(t^3+4)*(t^2) with respect to t	$\int \frac{1}{t^{3} + 4} \cdot (t^{2}) d t$
27264	Evaluate the Integral	integral of 1/((x-2) square root of x^2-4x+20) with respect to x	$\int \frac{1}{(x - 2) \sqrt{x^{2} - 4 x + 20}} d x$
27265	Find the Derivative - d/d@VAR	f(x)=x^(1/9)	$f (x) = x^{\frac{1}{9}}$
27266	Find the Derivative - d/d@VAR	f(x)=e^(x^4+3x)	$f (x) = e^{x^{4} + 3 x}$
27267	Find the Derivative - d/d@VAR	f(x)=13e^x	$f (x) = 13 e^{x}$
27268	Evaluate the Integral	integral of 1/((s-1)^2) with respect to s	$\int \frac{1}{{(s - 1)}^{2}} d s$
27269	Evaluate the Integral	integral of 1/(u^4) with respect to u	$\int \frac{1}{u^{4}} d u$
27270	Evaluate the Integral	integral of 1/(sin(2x)^2cos(2x)^4) with respect to x	$\int \frac{1}{\sin^{2} (2 x) \cos^{4} (2 x)} d x$
27271	Evaluate the Integral	integral of 1/( square root of x^2+8x+25) with respect to x	$\int \frac{1}{\sqrt{x^{2} + 8 x + 25}} d x$
27272	Find the Derivative - d/dx	1/4	$\frac{1}{4}$
27273	Evaluate the Integral	integral of 1/( square root of 12x-x^2) with respect to x	$\int \frac{1}{\sqrt{12 x - x^{2}}} d x$
27274	Evaluate the Integral	integral from 4 to 9 of square root of 4x^2+4x+1 with respect to x	$\int_{4}^{9} \sqrt{4 x^{2} + 4 x + 1} d x$
27275	Evaluate the Integral	integral of 4sin(t)^2 with respect to t	$\int 4 \sin^{2} (t) d t$
27276	Evaluate the Integral	integral of 4sin(x)^3 with respect to x	$\int 4 \sin^{3} (x) d x$
27277	Evaluate the Integral	integral of 4t^4e^(-t^5) with respect to t	$\int 4 t^{4} e^{- t^{5}} d t$
27278	Evaluate the Integral	integral of 4tan(x)^3 with respect to x	$\int 4 \tan^{3} (x) d x$
27279	Evaluate the Integral	integral of 4x^3(7x^4+12)^3 with respect to x	$\int 4 x^{3} {(7 x^{4} + 12)}^{3} d x$
27280	Evaluate the Integral	integral of 4x^4 with respect to x	$\int 4 x^{4} d x$
27281	Evaluate the Integral	integral of 4x^2(x^4+8) with respect to x	$\int 4 x^{2} (x^{4} + 8) d x$
27282	Evaluate the Integral	integral of 4t^3-30t with respect to t	$\int 4 t^{3} - 30 t d t$
27283	Evaluate the Integral	integral of 4xe^(x^2) with respect to x	$\int 4 x e^{x^{2}} d x$
27284	Evaluate the Integral	integral of 4y^2 with respect to y	$\int 4 y^{2} d y$
27285	Evaluate the Integral	integral of 4xe^(4x) with respect to x	$\int 4 x e^{4 x} d x$
27286	Evaluate the Integral	integral of -4x-6sin(x) with respect to x	$\int - 4 x - 6 \sin (x) d x$
27287	Evaluate the Integral	integral of 4xsin(x) with respect to x	$\int 4 x \sin (x) d x$
27288	Evaluate the Integral	integral of 4ydy with respect to y	$\int 4 yds y d y$
27289	Evaluate the Integral	integral of 5(5x+7) with respect to x	$\int 5 (5 x + 7) d x$
27290	Evaluate the Integral	integral from -5 to 0 of (w^2)/2+2w-2 with respect to w	$\int_{- 5}^{0} \frac{w^{2}}{2} + 2 w - 2 d w$
27291	Evaluate the Integral	integral of 4x(x^2+30000)^(-2/3) with respect to x	$\int 4 x {(x^{2} + 30000)}^{- \frac{2}{3}} d x$
27292	Evaluate the Integral	integral of 4x(2x^2+3)^3 with respect to x	$\int 4 x {(2 x^{2} + 3)}^{3} d x$
27293	Evaluate the Integral	integral of 4x square root of x-1 with respect to x	$\int 4 x \sqrt{x - 1} d x$
27294	Evaluate the Integral	integral of 4x(x^2+26000)^(-2/3) with respect to x	$\int 4 x {(x^{2} + 26000)}^{- \frac{2}{3}} d x$
27295	Evaluate the Integral	integral of 4xsec(2x)^2 with respect to x	$\int 4 x \sec^{2} (2 x) d x$
27296	Evaluate the Integral	integral of 4x square root of x^2+1 with respect to x	$\int 4 x \sqrt{x^{2} + 1} d x$
27297	Evaluate the Integral	integral of 46+2.1xe^(-0.01x^2) with respect to x	$\int 46 + 2.1 x e^{- 0.01 x^{2}} d x$
27298	Evaluate the Integral	integral of 48t^7e^(-t^8) with respect to t	$\int 48 t^{7} e^{- t^{8}} d t$
27299	Evaluate the Integral	integral of 49-x^2 with respect to x	$\int 49 - x^{2} d x$
27300	Evaluate the Integral	integral of 4cos(2x) with respect to x	$\int 4 \cos (2 x) d x$