Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
83101	Evaluate the Integral	integral of (2x^13)/(x^14) with respect to x	$\int \frac{2 x^{13}}{x^{14}} d x$
83102	Evaluate the Limit	limit as x approaches 4 of (1-4/x)/(4-x)	$lim_{x \to 4} \frac{1 - \frac{4}{x}}{4 - x}$
83103	Find the Derivative - d/dx	y=4/3pix^3	$y = \frac{4}{3} π x^{3}$
83104	Find the Second Derivative	x- natural log of x	$x - \ln (x)$
83105	Find the Derivative - d/dx	y=7+5cos(0.503(x-6.75))	$y = 7 + 5 \cos (0.503 (x - 6.75))$
83106	Find Where Increasing/Decreasing	f(x) = fourth root of 3x^2+1	$f (x) = \sqrt[4]{3 x^{2} + 1}$
83107	Evaluate the Integral	integral of ( square root of x-x^-3)/(x^2) with respect to x	$\int \frac{\sqrt{x} - x^{- 3}}{x^{2}} d x$
83108	Find the Integral	1/(2x-4y^2)	$\frac{1}{2 x - 4 y^{2}}$
83109	Evaluate the Limit	limit as x approaches 0 of (f(x))/(f(x)+2)	$lim_{x \to 0} \frac{f (x)}{f (x) + 2}$
83110	Integrate Using u-Substitution	integral from 0 to 1 of x^2 square root of 3x^3+6 with respect to x	$\int_{0}^{1} x^{2} \sqrt{3 x^{3} + 6} d x$
83111	Find the Derivative - d/dt	1/3t^3-t	$\frac{1}{3} t^{3} - t$
83112	Find dy/dx	y=x^2(x-1)	$y = x^{2} (x - 1)$
83113	Evaluate the Limit	limit as x approaches infinity of (1+1/x)^(4x+7)	$lim_{x \to \infty} {(1 + \frac{1}{x})}^{4 x + 7}$
83114	Find dy/dx	y=-(-8x^2-1)^4	$y = - {(- 8 x^{2} - 1)}^{4}$
83115	Evaluate the Integral	integral from 0 to pi/2 of (sin(x))/(1-cos(x)) with respect to x	$\int_{0}^{\frac{π}{2}} \frac{\sin (x)}{1 - \cos (x)} d x$
83116	Find the Derivative - d/dx	y=(2x+cot(x))/(5+e^x)	$y = \frac{2 x + \cot (x)}{5 + e^{x}}$
83117	Evaluate the Limit	limit as x approaches 2/3 of (4-9x^2)/(2-3x)	$lim_{x \to \frac{2}{3}} \frac{4 - 9 x^{2}}{2 - 3 x}$
83118	Evaluate Using L'Hospital's Rule	limit as x approaches 3 of (x^2-3x)/(3e^(2x-6)-x)	$lim_{x \to 3} \frac{x^{2} - 3 x}{3 e^{2 x - 6} - x}$
83119	Evaluate the Integral	integral from -b/2 to b/2 of (h-(4h)/(b^2)x^2) with respect to x	$\int_{- \frac{b}{2}}^{\frac{b}{2}} (h - \frac{4 h}{b^{2}} x^{2}) d x$
83120	Evaluate the Limit	limit as x approaches c of -4*3/4	$lim_{x \to c} - 4 \cdot \frac{3}{4}$
83121	Find the Derivative - d/dθ	theta+cos(theta)	$θ + \cos (θ)$
83122	Integrate Using u-Substitution	integral of (x^3+2x)^5(6x^2+4) with respect to x	$\int {(x^{3} + 2 x)}^{5} (6 x^{2} + 4) d x$
83123	Find dy/dx	y = square root of x+1/( square root of x)	$y = \sqrt{x} + \frac{1}{\sqrt{x}}$
83124	Evaluate the Integral	integral from 0 to 1 of 2x^2u(x) with respect to x=1	$\int_{0}^{1} 2 x^{2} u (x) d x = 1$ ?
83125	Find the Antiderivative	f(x)=3cos(2x)	$f (x) = 3 \cos (2 x)$
83126	Evaluate the Integral	integral from 0 to 1 of x^3 square root of 3+x^2 with respect to x	$\int_{0}^{1} x^{3} \sqrt{3 + x^{2}} d x$
83127	Evaluate the Integral	integral from 0 to pi of sin(x)(1-cos(x))^2 with respect to x	$\int_{0}^{π} \sin (x) {(1 - \cos (x))}^{2} d x$
83128	Find dy/dx	y=(x^3+1)^5cos(4x^3)	$y = {(x^{3} + 1)}^{5} \cos (4 x^{3})$
83129	Find the Derivative - d/dx	y=e^6x	$y = e^{6} x$
83130	Evaluate the Integral	integral of (5 fourth root of x)/2 with respect to x	$\int \frac{5 \sqrt[4]{x}}{2} d x$
83131	Find the Integral	xe^(-x)dx	$x e^{- x} d x$
83132	Find dy/dx	2y^2+3-y^3+x^3=y	$2 y^{2} + 3 - y^{3} + x^{3} = y$
83133	Find the Antiderivative	f(x)=1-1/(x^4)	$f (x) = 1 - \frac{1}{x^{4}}$
83134	Find the Derivative - d/dx	\|x\|+2\|1-x\|	$\| x \| + 2 \| 1 - x \|$
83135	Find the Center and Radius	x^2+y^2+25=0	$x^{2} + y^{2} + 25 = 0$
83136	Find dy/dx	y=3sin(2x)	$y = 3 \sin (2 x)$
83137	Find dy/dx	cos(x^2+y)=x	$\cos (x^{2} + y) = x$
83138	Evaluate the Integral	integral of (5 square root of x)/2 with respect to x	$\int \frac{5 \sqrt{x}}{2} d x$
83139	Find the Antiderivative	y/x	$\frac{y}{x}$
83140	Find the Derivative of the Integral	F(x) = integral from x^3 to x^2 of cos(t) with respect to t	$F (x) = \int_{x^{3}}^{x^{2}} \cos (t) d t$
83141	Evaluate the Integral	integral from 1 to 2 of x square root of x^2-1 with respect to x	$\int_{1}^{2} x \sqrt{x^{2} - 1} d x$
83142	Find the Antiderivative	e^pi	$e^{π}$
83143	Find dy/dx	y=e^(-x)+2xe^(-x)+x^2e^(-x)	$y = e^{- x} + 2 x e^{- x} + x^{2} e^{- x}$
83144	Find Where Increasing/Decreasing	y=1200*(1+0.3)^t	$y = 1200 \cdot {(1 + 0.3)}^{t}$
83145	Find the Antiderivative	f(x)=3/( square root of x)+x^2	$f (x) = \frac{3}{\sqrt{x}} + x^{2}$
83146	Evaluate Using L'Hospital's Rule	limit as x approaches 2 of (2cos(4-2x)-x)/(x^2-4)	$lim_{x \to 2} \frac{2 \cos (4 - 2 x) - x}{x^{2} - 4}$
83147	Find dy/dx	square root of 2x+y=x	$\sqrt{2 x + y} = x$
83148	Find dy/dx	y=x natural log of x-x	$y = x \ln (x) - x$
83149	Find the Local Maxima and Minima	f(x)=-1/2x^4+2x^3+28x^2+18	$f (x) = - \frac{1}{2} x^{4} + 2 x^{3} + 28 x^{2} + 18$
83150	Evaluate the Integral	integral of 16x^2 cube root of 7-4x^3 with respect to x	$\int 16 x^{2} \sqrt[3]{7 - 4 x^{3}} d x$
83151	Evaluate the Integral	integral of (x^2-1)/( cube root of x) with respect to x	$\int \frac{x^{2} - 1}{\sqrt[3]{x}} d x$
83152	Find the Antiderivative	f(x)=27x^2+cos(x)	$f (x) = 27 x^{2} + \cos (x)$
83153	Find the Derivative - d/dx	tan(x)sin(x)	$\tan (x) \sin (x)$
83154	Find the Maximum/Minimum Value	f(x)=1/2x^4-4x^3+8x^2+46	$f (x) = \frac{1}{2} x^{4} - 4 x^{3} + 8 x^{2} + 46$
83155	Evaluate the Integral	integral of (1+cos(x))/(x+sin(x)) with respect to x	$\int \frac{1 + \cos (x)}{x + \sin (x)} d x$
83156	Evaluate Using L'Hospital's Rule	limit as r approaches 0 from the right of -11(r/3) natural log of r/3	$lim_{r \to 0^{+}} - 11 (\frac{r}{3}) \ln (\frac{r}{3})$
83157	Find the Antiderivative	tan(2x)^2	$\tan^{2} (2 x)$
83158	Find the Derivative - d/dy	x/(2y)	$\frac{x}{2 y}$
83159	Find the Maximum/Minimum Value	y=x+1/(4x)	$y = x + \frac{1}{4 x}$
83160	Find the Derivative - d/dX	arctan(4X)	$\arctan (4 X)$
83161	Find the Derivative - d/dx	y=e^(7x^2+x)	$y = e^{7 x^{2} + x}$
83162	Evaluate the Limit	limit as x approaches negative infinity of (4x^5+1)/(x+x^3)	$lim_{x \to - \infty} \frac{4 x^{5} + 1}{x + x^{3}}$
83163	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (3 natural log of 3x-2)/(5x-5)	$lim_{x \to 1} \frac{3 \ln (3 x - 2)}{5 x - 5}$
83164	Find the Derivative of the Integral	integral from 0 to square root of x of t with respect to t	$\int_{0}^{\sqrt{x}} t d t$
83165	Find dy/dx	y=sin(4x)-8x^2+9x+pi	$y = \sin (4 x) - 8 x^{2} + 9 x + π$
83166	Find the Antiderivative	4/(x^2)+2x-3x^2	$\frac{4}{x^{2}} + 2 x - 3 x^{2}$
83167	Find the Antiderivative	1/( square root of X^3)	$\frac{1}{\sqrt{X^{3}}}$
83168	Find dx/dy	y=x natural log of x	$y = x \ln (x)$
83169	Evaluate the Limit	limit as x approaches infinity of 1/x+4cos(5/x)	$lim_{x \to \infty} \frac{1}{x} + 4 \cos (\frac{5}{x})$
83170	Find the Integral	xe^(2x)dx	$x e^{2 x} d x$
83171	Find the Derivative - d/dx	x-x^2cos(x)	$x - x^{2} \cos (x)$
83172	Find dy/dx	4x=-2y^2+xy	$4 x = - 2 y^{2} + x y$
83173	Evaluate the Limit	limit as x approaches negative infinity of (1+1/x)^x	$lim_{x \to - \infty} {(1 + \frac{1}{x})}^{x}$
83174	Find the Antiderivative	(x+1)/(x^2-3x+2)	$\frac{x + 1}{x^{2} - 3 x + 2}$
83175	Find the Antiderivative	f(x)=x square root of x-3/( square root of x)	$f (x) = x \sqrt{x} - \frac{3}{\sqrt{x}}$
83176	Integrate By Parts	integral from 0 to 2 of (3x^2-1)/(x^2) with respect to x	$\int_{0}^{2} \frac{3 x^{2} - 1}{x^{2}} d x$
83177	Find the Antiderivative	1/((1+x)(1-2x))	$\frac{1}{(1 + x) (1 - 2 x)}$
83178	Find the Maximum/Minimum Value	y=1/3x^3+5/2x^2+6x+8	$y = \frac{1}{3} x^{3} + \frac{5}{2} x^{2} + 6 x + 8$
83179	Find the Derivative - d/dx	f^2(x)	$f^{2} (x)$
83180	Evaluate Using L'Hospital's Rule	limit as x approaches -2 of (3cos(x+2)+x)/(4 natural log of -3-2x+x^3)	$lim_{x \to - 2} \frac{3 \cos (x + 2) + x}{4 \ln (- 3 - 2 x) + x^{3}}$
83181	Find the Percentage Rate of Change	y=1/4(1.2)^t	$y = \frac{1}{4} {(1.2)}^{t}$
83182	Find the Derivative - d/dx	e^(xy)=e^(4x)-e^(5y)	$e^{x y} = e^{4 x} - e^{5 y}$
83183	Find the Antiderivative	square root of 2x-x^2	$\sqrt{2 x - x^{2}}$
83184	Find Where Increasing/Decreasing	f(x)=2 cube root of x-3-1	$f (x) = 2 \sqrt[3]{x - 3} - 1$
83185	Find the Antiderivative	2x+3/(x^2)	$2 x + \frac{3}{x^{2}}$
83186	Evaluate the Limit	limit as x approaches 2 from the left of (\|2x-x^2\|)/(x-2)	$lim_{x \to 2^{-}} \frac{\| 2 x - x^{2} \|}{x - 2}$
83187	Find Where Increasing/Decreasing	f(x)=2x(x^2-3)	$f (x) = 2 x (x^{2} - 3)$
83188	Find the Derivative - d/dx	y/(y^2+x^2)	$\frac{y}{y^{2} + x^{2}}$
83189	Evaluate the Integral	integral of 1/(cot(u)) with respect to u	$\int \frac{1}{\cot (u)} d u$
83190	Evaluate the Integral	integral from -1 to 1 of (27/(x^4)-3) with respect to x	$\int_{- 1}^{1} (\frac{27}{x^{4}} - 3) d x$
83191	Evaluate the Integral	integral from 0 to pi/2 of cos(x) square root of 1+sin(x) with respect to x	$\int_{0}^{\frac{π}{2}} \cos (x) \sqrt{1 + \sin (x)} d x$
83192	Find dy/dx	cos(2x+3y^3)=3y^2	$\cos (2 x + 3 y^{3}) = 3 y^{2}$
83193	Find the Derivative - d/dx	300 cube root of x^2 fourth root of y-100x-150y+2021	$300 \sqrt[3]{x^{2}} \sqrt[4]{y} - 100 x - 150 y + 2021$
83194	Find the Antiderivative	square root of x+1/x	$\sqrt{x} + \frac{1}{x}$
83195	Find the Antiderivative	y=x	$y = x$
83196	Evaluate the Integral	integral from -pi/2 to -pi/4 of -2cot(x)csc(x)^2 with respect to x	$\int_{- \frac{π}{2}}^{- \frac{π}{4}} - 2 \cot (x) \csc^{2} (x) d x$
83197	Evaluate the Integral	integral of (sin(2x)+cos(2x)) with respect to x	$\int (\sin (2 x) + \cos (2 x)) d x$
83198	Find the Derivative - d/dx	y=(sec(x))/(1+tan(x))	$y = \frac{\sec (x)}{1 + \tan (x)}$
83199	Find the Derivative - d/dx	(3 square root of x)/2-2 square root of x^3	$\frac{3 \sqrt{x}}{2} - 2 \sqrt{x^{3}}$
83200	Find the Concavity	-1/3x^3+x^2	$- \frac{1}{3} x^{3} + x^{2}$