Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
80201	Find the Antiderivative	f(x)=4x^2+2x^(1/2)+ cube root of x	$f (x) = 4 x^{2} + 2 x^{\frac{1}{2}} + \sqrt[3]{x}$
80202	Evaluate the Summation	sum from i=1 to infinity of 4/7(7/6)^(i-1)	$\sum_{i = 1}^{\infty} \frac{4}{7} {(\frac{7}{6})}^{i - 1}$
80203	Solve the Differential Equation	(dy)/(dx)=2 square root of y+1cos(x)	$\frac{d y}{d x} = 2 \sqrt{y + 1} \cos (x)$
80204	Evaluate the Limit	limit as x approaches negative infinity of 3x^7-4x^9+3x^2	$lim_{x \to - \infty} 3 x^{7} - 4 x^{9} + 3 x^{2}$
80205	Find the Concavity	x^4+8x^3+18x^2	$x^{4} + 8 x^{3} + 18 x^{2}$
80206	Find the Derivative - d/dx	y=sech(x)tanh(x)	$y = sech (x) \tanh (x)$
80207	Verify the Differential Equation Solution	y'+y''=6e^(2x) , y=e^(2x)	$y' + y'' = 6 e^{2 x}$ , $y = e^{2 x}$
80208	Find the Derivative - d/dx	f(x)( cube root of 64x^6)/(x^5)	$f (x) \frac{\sqrt[3]{64 x^{6}}}{x^{5}}$
80209	Evaluate the Limit	limit as x approaches 0 of (3x+2x^-1)/(x+4x^-1)	$lim_{x \to 0} \frac{3 x + 2 x^{- 1}}{x + 4 x^{- 1}}$
80210	Find the Antiderivative	f(x)=-1/(x^2)	$f (x) = - \frac{1}{x^{2}}$
80211	Find the Antiderivative	1/(x^2)-x^2-1/3	$\frac{1}{x^{2}} - x^{2} - \frac{1}{3}$
80212	Evaluate the Integral	integral from 0 to 1 of x^4e^(2x^5-7) with respect to x	$\int_{0}^{1} x^{4} e^{2 x^{5} - 7} d x$
80213	Evaluate the Limit	limit as x approaches infinity of 3+5x^2+3x	$lim_{x \to \infty} 3 + 5 x^{2} + 3 x$
80214	Integrate Using Partial Fractions	integral of (x^5)/(x^3-1) with respect to x	$\int \frac{x^{5}}{x^{3} - 1} d x$
80215	Find the Antiderivative	x square root of x-4/( square root of x)	$x \sqrt{x} - \frac{4}{\sqrt{x}}$
80216	Find Where Increasing/Decreasing	x^4+8x^3+18x^2	$x^{4} + 8 x^{3} + 18 x^{2}$
80217	Find dy/dx	y=(4x^2-16)/(x-2)	$y = \frac{4 x^{2} - 16}{x - 2}$
80218	Find the Antiderivative	x/(cos(x)^2)	$\frac{x}{\cos^{2} (x)}$
80219	Evaluate the Limit	limit as x approaches -2 of ((x+3)^5-1)/(x^2-4)	$lim_{x \to - 2} \frac{{(x + 3)}^{5} - 1}{x^{2} - 4}$
80220	Find Where Increasing/Decreasing	f(x)=1/2*5^(-x)-1	$f (x) = \frac{1}{2} \cdot 5^{- x} - 1$
80221	Find the Derivative - d/dx	y=-2e^(2x^2-1)	$y = - 2 e^{2 x^{2} - 1}$
80222	Find Where Increasing/Decreasing	f(x)=(x-1)^(1/3)	$f (x) = {(x - 1)}^{\frac{1}{3}}$
80223	Find the Third Derivative	3^x+2021	$3^{x} + 2021$
80224	Find dy/dx	xy^2+(x^2)/y=5	$x y^{2} + \frac{x^{2}}{y} = 5$
80225	Find the Antiderivative	pi^2	$π^{2}$
80226	Find the Antiderivative	1/(x(x+1))	$\frac{1}{x (x + 1)}$
80227	Verify the Differential Equation Solution	y'=(3y)/x , y=x^3	$y' = \frac{3 y}{x}$ , $y = x^{3}$
80228	Find the Antiderivative	-3/(x^2)+4/(x^3)	$- \frac{3}{x^{2}} + \frac{4}{x^{3}}$
80229	Evaluate Using Summation Formulas	sum from k=1 to n of k^3	$\sum_{k = 1}^{n} k^{3}$
80230	Find the Antiderivative	4e^x+x^3	$4 e^{x} + x^{3}$
80231	Find the Derivative - d/dx	(d^43)/(dx^43)(cos(3x)+5^(2x))	$\frac{d^{43}}{d x^{43}} (\cos (3 x) + 5^{2 x})$
80232	Evaluate the Limit	limit as x approaches 0 of (e^x-1)/(x^4)	$lim_{x \to 0} \frac{e^{x} - 1}{x^{4}}$
80233	Find the Integral	6^(2x)*2dx	$6^{2 x} \cdot 2 d x$
80234	Find the Derivative - d/dx	y=-1/3(x^7+2x-9)	$y = - \frac{1}{3} (x^{7} + 2 x - 9)$
80235	Evaluate the Integral	integral of x^2 square root of 3x+2 with respect to x	$\int x^{2} \sqrt{3 x + 2} d x$
80236	Verify the Differential Equation Solution	y'=y-2x , y=3x	$y' = y - 2 x$ , $y = 3 x$
80237	Find the Antiderivative	f(x)=cos(x)^2	$f (x) = \cos^{2} (x)$
80238	Find the Maximum/Minimum Value	-2xe^(1-x^2)	$- 2 x e^{1 - x^{2}}$
80239	Evaluate the Integral	integral of sin(e^(2x))^4cos(e^(2x))e^(2x) with respect to x	$\int \sin^{4} (e^{2 x}) \cos (e^{2 x}) e^{2 x} d x$
80240	Find the Fourth Derivative	x+ square root of x+1	$x + \sqrt{x + 1}$
80241	Verify the Differential Equation Solution	y'=(3y)/x , y=3x	$y' = \frac{3 y}{x}$ , $y = 3 x$
80242	Find the Derivative - d/dx	y=1/(2^(4x))	$y = \frac{1}{2^{4 x}}$
80243	Evaluate the Limit	limit as x approaches infinity of square root of (x+2020)(x+2021)-x	$lim_{x \to \infty} \sqrt{(x + 2020) (x + 2021)} - x$
80244	Evaluate the Integral	integral of [12x^2+csc(3x)^2] with respect to x	$\int [12 x^{2} + \csc^{2} (3 x)] d x$
80245	Find the Antiderivative	x*e^(x^2)	$x \cdot e^{x^{2}}$
80246	Evaluate the Integral	integral of 5x^2sec(2x^3-6)^2 with respect to x	$\int 5 x^{2} \sec^{2} (2 x^{3} - 6) d x$
80247	Find the Antiderivative	(2^x-1)/(e^x)	$\frac{2^{x} - 1}{e^{x}}$
80248	Evaluate the Integral	integral of (x^3-4x-1)/(2x^3) with respect to x	$\int \frac{x^{3} - 4 x - 1}{2 x^{3}} d x$
80249	Find the Integral	5^xdx	$5^{x} d x$
80250	Find the Derivative - d/dy	natural log of 1+x^2+2y^2	$\ln (1 + x^{2} + 2 y^{2})$
80251	Evaluate the Integral	integral of 5x( square root of x-x^2) with respect to x	$\int 5 x (\sqrt{x} - x^{2}) d x$
80252	Evaluate the Summation	sum from n=0 to 4 of nx+2	$\sum_{n = 0}^{4} n x + 2$
80253	Find the Maximum/Minimum Value	f(x)=-x^4+2x^2-x-2	$f (x) = - x^{4} + 2 x^{2} - x - 2$
80254	Find the Antiderivative	(2x+3)/( square root of x)	$\frac{2 x + 3}{\sqrt{x}}$
80255	Find Where Increasing/Decreasing	f(x) = square root of x-4	$f (x) = \sqrt{x} - 4$
80256	Verify the Differential Equation Solution	y'+2y=0 , y=3e^(-2x)	$y' + 2 y = 0$ , $y = 3 e^{- 2 x}$
80257	Find the Slope of the Tangent Line at (1/2,8)	f(t)=t^-3 ;, (1/2,8)	$f (t) = t^{- 3}$ ;, $(\frac{1}{2}, 8)$
80258	Find the Antiderivative	f(x)=-3x^-4+10x^(2/3)	$f (x) = - 3 x^{- 4} + 10 x^{\frac{2}{3}}$
80259	Evaluate the Integral	integral of (x^3+3)^3x^5 with respect to x	$\int {(x^{3} + 3)}^{3} x^{5} d x$
80260	Find the Third Derivative	y=3x^-2+4x^-1+x	$y = 3 x^{- 2} + 4 x^{- 1} + x$
80261	Find the Derivative - d/dx	d/(dx)((x^2+4)(2x^3+7x))	$\frac{d}{d x} ((x^{2} + 4) (2 x^{3} + 7 x))$
80262	Evaluate the Integral	integral of (4x^-2+6 square root of x-6/(x^2)) with respect to x	$\int (4 x^{- 2} + 6 \sqrt{x} - \frac{6}{x^{2}}) d x$
80263	Evaluate the Limit	limit as x approaches pi/2 of 2x-cos(x)	$lim_{x \to \frac{π}{2}} 2 x - \cos (x)$
80264	Find the Integral	(-9x^2+10x)dx	$(- 9 x^{2} + 10 x) d x$
80265	Find the Antiderivative	f(x)=sin(x)^2	$f (x) = \sin^{2} (x)$
80266	Solve the Differential Equation	(y/x+ natural log of y)dx+(x/y+ natural log of x)dy=0	$(\frac{y}{x} + \ln (y)) d x + (\frac{x}{y} + \ln (x)) d y = 0$
80267	Evaluate the Integral	integral of x^2-x+x^-1 with respect to x	$\int x^{2} - x + x^{- 1} d x$
80268	Evaluate the Integral	integral from 0 to 2 of (x^3+1)^(1/2)x^2 with respect to x	$\int_{0}^{2} {(x^{3} + 1)}^{\frac{1}{2}} x^{2} d x$
80269	Find the Antiderivative	f(x)=1/(3^x)	$f (x) = \frac{1}{3^{x}}$
80270	Evaluate the Integral	integral of sin(x)^2cos(x)^3+2x with respect to x	$\int \sin^{2} (x) \cos^{3} (x) + 2 x d x$
80271	Find the Critical Points	f(x)=x^3+ax	$f (x) = x^{3} + a x$
80272	Evaluate the Integral	integral from 0 to 1 of 1/(1-x) with respect to x	$\int_{0}^{1} \frac{1}{1 - x} d x$
80273	Find the Second Derivative	x+ square root of x+1	$x + \sqrt{x + 1}$
80274	Evaluate the Integral	integral of 5x(2x+5)(x-3) with respect to x	$\int 5 x (2 x + 5) (x - 3) d x$
80275	Evaluate the Summation	sum from i=1 to 12 of 2i^2-7	$\sum_{i = 1}^{12} 2 i^{2} - 7$
80276	Find Where Increasing/Decreasing	-x^4-8x^3-18x^2	$- x^{4} - 8 x^{3} - 18 x^{2}$
80277	Find the Derivative of the Integral	integral from 1 to x^2+1 of (2t+2)/( square root of t+1) with respect to t	$\int_{1}^{x^{2} + 1} \frac{2 t + 2}{\sqrt{t + 1}} d t$
80278	Find the Inflection Points	f(x)=-1/6x^6-x^5+5x^4	$f (x) = - \frac{1}{6} x^{6} - x^{5} + 5 x^{4}$
80279	Find the Antiderivative	x^2e^(-x)	$x^{2} e^{- x}$
80280	Evaluate the Limit	limit as x approaches square root of 2 of (2x^2+1)(7x^2+13)	$lim_{x \to \sqrt{2}} (2 x^{2} + 1) (7 x^{2} + 13)$
80281	Find the Third Derivative	x+ square root of x+1	$x + \sqrt{x + 1}$
80282	Find the Inflection Points	f(x)=1/6x^6+x^5-5x^4	$f (x) = \frac{1}{6} x^{6} + x^{5} - 5 x^{4}$
80283	Verify the Differential Equation Solution	y'=3x^2 , y=x^3-4	$y' = 3 x^{2}$ , $y = x^{3} - 4$
80284	Evaluate the Limit	limit as x approaches infinity of (5+x^-2)/(1+3x^-2)	$lim_{x \to \infty} \frac{5 + x^{- 2}}{1 + 3 x^{- 2}}$
80285	Find the Antiderivative	(e^x)/(e^x+1)	$\frac{e^{x}}{e^{x} + 1}$
80286	Evaluate the Integral	integral from pi/6 to pi/2 of csc(t)*cot(t) with respect to t	$\int_{\frac{π}{6}}^{\frac{π}{2}} \csc (t) \cdot \cot (t) d t$
80287	Solve the Differential Equation	(1-x)y'=y^2	$(1 - x) y' = y^{2}$
80288	Evaluate the Integral	integral of 10xsin(5x^2+2) with respect to x	$\int 10 x \sin (5 x^{2} + 2) d x$
80289	Find the Antiderivative	f(x) = square root of x-2/( square root of x)	$f (x) = \sqrt{x} - \frac{2}{\sqrt{x}}$
80290	Evaluate the Limit	limit as x approaches 0 of ((2-3x)^7-128)/(4x)	$lim_{x \to 0} \frac{{(2 - 3 x)}^{7} - 128}{4 x}$
80291	Find the Inflection Points	f(x)=2/5x^6-7x^4	$f (x) = \frac{2}{5} x^{6} - 7 x^{4}$
80292	Find the Antiderivative	cos(x/2)^2	$\cos^{2} (\frac{x}{2})$
80293	Find the Concavity	f(x)=-1/6x^6+2x^5-5x^4	$f (x) = - \frac{1}{6} x^{6} + 2 x^{5} - 5 x^{4}$
80294	Evaluate the Integral	integral from 0 to 1 of 2x^2u(x) with respect to x=1	$\int_{0}^{1} 2 x^{2} u (x) d x = 1$
80295	Find the Derivative - d/dx	y=(3x^2)/2+1	$y = \frac{3 x^{2}}{2} + 1$
80296	Evaluate the Summation	sum from i=1 to 12 of i+3	$\sum_{i = 1}^{12} i + 3$
80297	Find the Antiderivative	x^2-3x+1/x	$x^{2} - 3 x + \frac{1}{x}$
80298	Find the Antiderivative	(cos(x))/(3+sin(x))	$\frac{\cos (x)}{3 + \sin (x)}$
80299	Find the Antiderivative	square root of x+2x^2 square root of x	$\sqrt{x} + 2 x^{2} \sqrt{x}$
80300	Evaluate the Integral	integral of (8arctan(2x))/(1+4x^2) with respect to x	$\int \frac{8 \arctan (2 x)}{1 + 4 x^{2}} d x$