Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
9201	Find the Derivative of the Integral	integral of x^3 square root of x^2+1 with respect to x	$\int x^{3} \sqrt{x^{2} + 1} d x$
9202	Find the Derivative of the Integral	integral of x^3sin(x) with respect to x	$\int x^{3} \sin (x) d x$
9203	Find the Derivative of the Integral	integral from pi/4 to x of cos(2t) with respect to t	$\int_{\frac{π}{4}}^{x} \cos (2 t) d t$
9204	Find the Derivative of the Integral	integral of e^( square root of x) with respect to x	$\int e^{\sqrt{x}} d x$
9205	Find the Derivative of the Integral	integral from 0 to 24 of square root of 6x with respect to x	$\int_{0}^{24} \sqrt{6 x} d x$
9206	Find the Derivative of the Integral	integral from 0 to 7 of square root of 7x with respect to x	$\int_{0}^{7} \sqrt{7 x} d x$
9207	Find the Derivative of the Integral	integral from 0 to x of sin(t^2) with respect to t	$\int_{0}^{x} \sin (t^{2}) d t$
9208	Find the Derivative of the Integral	integral from 0 to 8 of square root of 8x with respect to x	$\int_{0}^{8} \sqrt{8 x} d x$
9209	Find the Derivative of the Integral	integral from 0 to pi of cos(nt) with respect to t	$\int_{0}^{π} \cos (n t) d t$
9210	Find the Derivative of the Integral	integral from 0 to x of e^(-t^2) with respect to t	$\int_{0}^{x} e^{- t^{2}} d t$
9211	Find the Derivative - d/dx	1/(cos(x))	$\frac{1}{\cos (x)}$
9212	Evaluate the Integral	integral of 4^x with respect to x	$\int 4^{x} d x$
9213	Evaluate the Limit	limit as y approaches -3 of square root of (y^2-9)/(2y^2+7y+3)	$lim_{y \to - 3} \sqrt{\frac{y^{2} - 9}{2 y^{2} + 7 y + 3}}$
9214	Find the Derivative - d/dx	y=(sin(2x)^3( square root of x+1))/(tan(x)^2)	$y = \frac{\sin^{3} (2 x) (\sqrt{x + 1})}{\tan^{2} (x)}$
9215	Evaluate the Integral	integral of 2^(-x) with respect to x	$\int 2^{- x} d x$
9216	Evaluate the Integral	integral of 1/t*(2/(t^2)-3/(t^3)) with respect to t	$\int \frac{1}{t} \cdot (\frac{2}{t^{2}} - \frac{3}{t^{3}}) d t$
9217	Evaluate the Integral	integral of 1/(x-11) with respect to x	$\int \frac{1}{x - 11} d x$
9218	Evaluate the Integral	integral of (9x+5)^2 with respect to x	$\int {(9 x + 5)}^{2} d x$
9219	Evaluate the Integral	integral from 0 to 4 of square root of x with respect to x	$\int_{0}^{4} \sqrt{x} d x$
9220	Evaluate the Integral	integral of e^(4x)cos(5x) with respect to x	$\int e^{4 x} \cos (5 x) d x$
9221	Evaluate	18e^(-0.2*5)	$18 e^{- 0.2 \cdot 5}$
9222	Evaluate the Integral	integral of e^xcos(2x) with respect to x	$\int e^{x} \cos (2 x) d x$
9223	Find the Inflection Points	f(x)=4x^3-9x^4	$f (x) = 4 x^{3} - 9 x^{4}$
9224	Evaluate the Integral	integral of (sec(x)tan(x))/(9+4sec(x)^2) with respect to x	$\int \frac{\sec (x) \tan (x)}{9 + 4 \sec^{2} (x)} d x$
9225	Evaluate the Integral	integral of (sin(2x))/(3+cos(2x)) with respect to x	$\int \frac{\sin (2 x)}{3 + \cos (2 x)} d x$
9226	Evaluate the Summation	sum from k=1 to 13 of k	$\sum_{k = 1}^{13} k$
9227	Evaluate the Integral	integral from pi/4 to pi/3 of sec(x)^2 with respect to x	$\int_{\frac{π}{4}}^{\frac{π}{3}} \sec^{2} (x) d x$
9228	Evaluate the Integral	integral of e^(r/2) with respect to r	$\int e^{\frac{r}{2}} d r$
9229	Evaluate the Integral	integral of 6^(sin(x))cos(x) with respect to x	$\int 6^{\sin (x)} \cos (x) d x$
9230	Evaluate the Integral	integral of (cos(x))/( square root of 9-sin(x)^2) with respect to x	$\int \frac{\cos (x)}{\sqrt{9 - \sin^{2} (x)}} d x$
9231	Evaluate the Integral	integral from 0 to 1 of (e^x)/(1+e^x) with respect to x	$\int_{0}^{1} \frac{e^{x}}{1 + e^{x}} d x$
9232	Find the Local Maxima and Minima	e^(4x)+e^(-x)	$e^{4 x} + e^{- x}$
9233	Evaluate the Integral	integral from 0 to pi/4 of cos(2x)sin(sin(2x)) with respect to x	$\int_{0}^{\frac{π}{4}} \cos (2 x) \sin (\sin (2 x)) d x$
9234	Find dy/dx	y=x^4e^x	$y = x^{4} e^{x}$
9235	Find dy/dx	y=1/( square root of x)	$y = \frac{1}{\sqrt{x}}$
9236	Find dy/db	y=e^(ax)sin(bx)	$y = e^{a x} \sin (b x)$
9237	Find dy/dx	e^(x/y)=7x-y	$e^{\frac{x}{y}} = 7 x - y$
9238	Evaluate the Integral	integral of sec(2x)+tan(2x) with respect to x	$\int \sec (2 x) + \tan (2 x) d x$
9239	Find the Derivative - d/d@VAR	f(x)=x^(1/8)	$f (x) = x^{\frac{1}{8}}$
9240	Find the Derivative - d/d@VAR	c(x)=100/(100-x)	$c (x) = \frac{100}{100 - x}$
9241	Find the Inflection Points	1/2x^4+2x^3	$\frac{1}{2} x^{4} + 2 x^{3}$
9242	Find the Derivative - d/dy	(y^4)/8+1/(4y^2)	$\frac{y^{4}}{8} + \frac{1}{4 y^{2}}$
9243	Evaluate the Integral	integral of x^6 natural log of x with respect to x	$\int x^{6} \ln (x) d x$
9244	Evaluate the Limit	limit as t approaches -5 of (t^3+125)/(t+5)	$lim_{t \to - 5} \frac{t^{3} + 125}{t + 5}$
9245	Evaluate the Integral	integral of x^2e^(6x) with respect to x	$\int x^{2} e^{6 x} d x$
9246	Evaluate the Integral	integral of x/(x^4+16) with respect to x	$\int \frac{x}{x^{4} + 16} d x$
9247	Evaluate the Limit	limit as x approaches 5 of (sin(x-5))/(x^2-25)	$lim_{x \to 5} \frac{\sin (x - 5)}{x^{2} - 25}$
9248	Evaluate the Limit	limit as x approaches negative infinity of (1-e^x)/(1+e^x)	$lim_{x \to - \infty} \frac{1 - e^{x}}{1 + e^{x}}$
9249	Evaluate the Integral	integral of x/( square root of x-9) with respect to x	$\int \frac{x}{\sqrt{x - 9}} d x$
9250	Evaluate the Limit	limit as x approaches infinity of ( natural log of x)/x	$lim_{x \to \infty} \frac{\ln (x)}{x}$
9251	Simplify	square root of 9ab^3	$\sqrt{9 a b^{3}}$
9252	Evaluate the Integral	integral of square root of ax+b with respect to x	$\int \sqrt{a x + b} d x$
9253	Evaluate the Integral	integral of square root of y(4-3y-2y^2) with respect to y	$\int \sqrt{y} (4 - 3 y - 2 y^{2}) d y$
9254	Evaluate the Integral	integral of u^2sin(2u) with respect to u	$\int u^{2} \sin (2 u) d u$
9255	Evaluate the Integral	integral of 5/((6x+4)^2+2) with respect to x	$\int \frac{5}{{(6 x + 4)}^{2} + 2} d x$
9256	Evaluate the Integral	integral of x(x+7)^6 with respect to x	$\int x {(x + 7)}^{6} d x$
9257	Evaluate	arctan(infinity)	$\arctan (\infty)$
9258	Simplify	log base 2 of 5+ log base 2 of x^2-1- log base 2 of x-1	$\log_{2} (5) + \log_{2} (x^{2} - 1) - \log_{2} (x - 1)$
9259	Evaluate the Limit	limit as x approaches infinity of (1-x^2)/(x^3-x+1)	$lim_{x \to \infty} \frac{1 - x^{2}}{x^{3} - x + 1}$
9260	Find the Derivative - d/dx	y = natural log of square root of x+1	$y = \ln (\sqrt{x + 1})$
9261	Find dy/dx	x^2+xy-y^2=11	$x^{2} + x y - y^{2} = 11$
9262	Evaluate	20e^(-0.2*5)	$20 e^{- 0.2 \cdot 5}$
9263	Evaluate the Integral	integral of 1/(u^2) with respect to u	$\int \frac{1}{u^{2}} d u$
9264	Evaluate the Integral	integral from 1 to 4 of square root of 16x^5 with respect to x	$\int_{1}^{4} \sqrt{16 x^{5}} d x$
9265	Evaluate the Integral	integral from 1 to 8 of 8/(3x^5) with respect to x	$\int_{1}^{8} \frac{8}{3 x^{5}} d x$
9266	Evaluate the Integral	integral from 1 to 4 of 3 square root of x with respect to x	$\int_{1}^{4} 3 \sqrt{x} d x$
9267	Find the Critical Points	f(x)=x^2-10x	$f (x) = x^{2} - 10 x$
9268	Evaluate the Integral	integral from 0 to 2 of \|z-z^2\| with respect to z	$\int_{0}^{2} \| z - z^{2} \| d z$
9269	Evaluate the Integral	integral from 0 to 2 of (2t)/((t-3)^2) with respect to t	$\int_{0}^{2} \frac{2 t}{{(t - 3)}^{2}} d t$
9270	Evaluate the Integral	integral from 0 to 1 of 35x^4e^(x^5) with respect to x	$\int_{0}^{1} 35 x^{4} e^{x^{5}} d x$
9271	Evaluate the Integral	integral from 0 to 1 of y(y^2+1)^5 with respect to y	$\int_{0}^{1} y {(y^{2} + 1)}^{5} d y$
9272	Evaluate the Limit	limit as x approaches infinity of ( square root of 9x^2+4)/(6x+1)	$lim_{x \to \infty} \frac{\sqrt{9 x^{2} + 4}}{6 x + 1}$
9273	Find the Difference Quotient	f(x)=x/(6-x)	$f (x) = \frac{x}{6 - x}$
9274	Find the Antiderivative	x^(-1/2)	$x^{- \frac{1}{2}}$
9275	Graph	y=x(x-4)^3	$y = x {(x - 4)}^{3}$
9276	Evaluate the Integral	integral from 0 to 5 of 3000e^(-0.05x) with respect to x	$\int_{0}^{5} 3000 e^{- 0.05 x} d x$
9277	Evaluate the Integral	integral from 0 to 1 of 2x with respect to x	$\int_{0}^{1} 2 x d x$
9278	Evaluate the Integral	integral from 0 to 9 of (2t^2+t^2 square root of t-1)/(t^2) with respect to t	$\int_{0}^{9} \frac{2 t^{2} + t^{2} \sqrt{t} - 1}{t^{2}} d t$
9279	Evaluate the Summation	sum from i=7 to 16 of 2i-12	$\sum_{i = 7}^{16} 2 i - 12$
9280	Evaluate the Integral	integral from -1 to 1 of t^3-9t with respect to t	$\int_{- 1}^{1} t^{3} - 9 t d t$
9281	Find the Arc Length	f(x)=x^2+2x , 0<x<6	$f (x) = x^{2} + 2 x$ , $0 < x < 6$
9282	Find the Arc Length	f(x)=(4/5)x^(5/4) , [0,4]	$f (x) = (\frac{4}{5}) x^{\frac{5}{4}}$ , $[0, 4]$
9283	Find the Arc Length	y=4-x^2 , [-2,2]	$y = 4 - x^{2}$ , $[- 2, 2]$
9284	Find the Sine Given the Point	(0.36,0.15)	$(0.36, 0.15)$
9285	Find the Average Value of the Derivative	y=x^3 , [0,5]	$y = x^{3}$ , $[0, 5]$
9286	Find the Average Value of the Derivative	f(x)=2 square root of x , [4,9]	$f (x) = 2 \sqrt{x}$ , $[4, 9]$
9287	Find the Average Value of the Derivative	f(x)=x^3+1 , [2,3]	$f (x) = x^{3} + 1$ , $[2, 3]$
9288	Check if Differentiable Over an Interval	f(x)=x^2+2x , (0,6)	$f (x) = x^{2} + 2 x$ , $(0, 6)$
9289	Use the Limit Definition to Find the Derivative	f(x)=1/( square root of x)	$f (x) = \frac{1}{\sqrt{x}}$
9290	Find the Derivative - d/d@VAR	f(x) = square root of x+9	$f (x) = \sqrt{x + 9}$
9291	Use the Limit Definition to Find the Derivative	f(x)=3x^2	$f (x) = 3 x^{2}$
9292	Use the Limit Definition to Find the Derivative	f(x)=x^3-5	$f (x) = x^{3} - 5$
9293	Use the Limit Definition to Find the Derivative	f(x)=x^2-1	$f (x) = x^{2} - 1$
9294	Use the Limit Definition to Find the Derivative	f(x)=x^2-3x	$f (x) = x^{2} - 3 x$
9295	Use the Limit Definition to Find the Derivative	f(x)=2x^3	$f (x) = 2 x^{3}$
9296	Use the Limit Definition to Find the Derivative	f(x)=2x+4	$f (x) = 2 x + 4$
9297	Use the Limit Definition to Find the Derivative	f(x)=2x+7	$f (x) = 2 x + 7$
9298	Use the Limit Definition to Find the Derivative	f(x)=x^(2/3)	$f (x) = x^{\frac{2}{3}}$
9299	Use the Limit Definition to Find the Derivative	f(x) = square root of x-2	$f (x) = \sqrt{x - 2}$
9300	Use the Limit Definition to Find the Derivative	f(x) = square root of x-5	$f (x) = \sqrt{x - 5}$