Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
83901	Evaluate the Integral	integral of (a+bx^2)/( square root of 3ax+bx^3) with respect to a	$\int \frac{a + b x^{2}}{\sqrt{3 a x + b x^{3}}} d a$
83902	Evaluate the Integral	integral from -1 to 1 of e^x-(x^2-1) with respect to x	$\int_{- 1}^{1} e^{x} - (x^{2} - 1) d x$
83903	Find dy/dx	5x^3=y^3-4y	$5 x^{3} = y^{3} - 4 y$
83904	Evaluate the Integral	integral of 2 square root of x square root of 1+(1/( square root of x))^2 with respect to x	$\int 2 \sqrt{x} \sqrt{1 + {(\frac{1}{\sqrt{x}})}^{2}} d x$
83905	Find the Maximum/Minimum Value	f(x)=x^5-4x^3+x^2+2	$f (x) = x^{5} - 4 x^{3} + x^{2} + 2$
83906	Evaluate the Integral	integral of 20x^3sec(5x^4-1)tan(5x^4-1) with respect to x	$\int 20 x^{3} \sec (5 x^{4} - 1) \tan (5 x^{4} - 1) d x$
83907	Evaluate the Summation	6 sum from t=1 to 4 of 9-2t^2	$6 \sum_{t = 1}^{4} 9 - 2 t^{2}$
83908	Find the Maximum/Minimum Value	y=3cos(x)+1	$y = 3 \cos (x) + 1$
83909	Evaluate the Limit	limit as x approaches negative infinity of (7x^2-9)/(4x+3)	$lim_{x \to - \infty} \frac{7 x^{2} - 9}{4 x + 3}$
83910	Find the Maximum/Minimum Value	f(x)=sin(x)-cos(x)	$f (x) = \sin (x) - \cos (x)$
83911	Find the Derivative - d/dx	x^4-5x^3y^2+2y^4	$x^{4} - 5 x^{3} y^{2} + 2 y^{4}$
83912	Evaluate the Integral	integral of (3x^4-5x^2+x) with respect to x	$\int (3 x^{4} - 5 x^{2} + x) d x$
83913	Evaluate the Limit	limit as x approaches negative infinity of square root of x^2+x+1+x	$lim_{x \to - \infty} \sqrt{x^{2} + x + 1} + x$
83914	Find the Derivative - d/dx	1/( log of x)	$\frac{1}{\log (x)}$
83915	Find the Maximum/Minimum Value	y=1/2tan(2x)	$y = \frac{1}{2} \tan (2 x)$
83916	Find the Antiderivative	f(x) = square root of 2cos(x)	$f (x) = \sqrt{2} \cos (x)$
83917	Find the Derivative - d/dx	4^(3x^2)	$4^{3 x^{2}}$
83918	Evaluate the Limit	limit as t approaches 0 of (sin(t))/(e^(3t)-1)	$lim_{t \to 0} \frac{\sin (t)}{e^{3 t} - 1}$
83919	Integrate Using u-Substitution	integral from 3 to 4 of x square root of x-3 with respect to x	$\int_{3}^{4} x \sqrt{x - 3} d x$
83920	Integrate By Parts	integral of 1/(x natural log of x) with respect to x	$\int \frac{1}{x \ln (x)} d x$
83921	Find the Slope of the Tangent Line at x=4	y=9x^(5/2)-7x^(3/2) , x=4	$y = 9 x^{\frac{5}{2}} - 7 x^{\frac{3}{2}}$ , $x = 4$
83922	Evaluate the Integral	integral from -2 to -(2 square root of 3)/3 of 9/(x square root of 4x^2-4) with respect to x	$\int_{- 2}^{- \frac{2 \sqrt{3}}{3}} \frac{9}{x \sqrt{4 x^{2} - 4}} d x$
83923	Evaluate the Integral	integral of (x^3)/((x+1)^2) with respect to x	$\int \frac{x^{3}}{{(x + 1)}^{2}} d x$
83924	Evaluate the Integral	integral of (12x^4+14x^3+x^2)/(x^2) with respect to x	$\int \frac{12 x^{4} + 14 x^{3} + x^{2}}{x^{2}} d x$
83925	Evaluate the Integral	integral of (4/(3t^2)+7/(2t)) with respect to x	$\int (\frac{4}{3 t^{2}} + \frac{7}{2 t}) d x$
83926	Find the Antiderivative	3 square root of x+x^2018	$3 \sqrt{x} + x^{2018}$
83927	Find the Derivative - d/dx	y=9sec(1/3x)	$y = 9 \sec (\frac{1}{3} x)$
83928	Evaluate the Limit	limit as x approaches 1 of (x^3+2x^2+3x)/x	$lim_{x \to 1} \frac{x^{3} + 2 x^{2} + 3 x}{x}$
83929	Evaluate the Limit	limit as x approaches infinity of (5x^2-3x+6)/(1+4x-7x^2)	$lim_{x \to \infty} \frac{5 x^{2} - 3 x + 6}{1 + 4 x - 7 x^{2}}$
83930	Find the Antiderivative	7*e^x	$7 \cdot e^{x}$
83931	Find Where Increasing/Decreasing	(x-2)/((x+3)^2)	$\frac{(x - 2)}{{(x + 3)}^{2}}$
83932	Evaluate the Limit	limit as x approaches 0 of (x+sin(x))^(1/x)	$lim_{x \to 0} {(x + \sin (x))}^{\frac{1}{x}}$
83933	Find the Derivative - d/dx	natural log of x^2y	$\ln (x^{2} y)$
83934	Evaluate the Integral	integral from 1 to 4 of (4/(x^2)+2x-3x^2) with respect to x	$\int_{1}^{4} (\frac{4}{x^{2}} + 2 x - 3 x^{2}) d x$
83935	Find the Antiderivative	natural log of x^2-x	$\ln (x^{2} - x)$
83936	Find the Antiderivative	8(4^x)	$8 (4^{x})$
83937	Find the Derivative - d/dx	(-4x^6+4x^5-3x^3)/(3x^2)	$\frac{- 4 x^{6} + 4 x^{5} - 3 x^{3}}{3 x^{2}}$
83938	Evaluate the Limit	limit as x approaches infinity of (x^2)/(e^(2x))	$lim_{x \to \infty} \frac{x^{2}}{e^{2 x}}$
83939	Evaluate the Integral	integral of (2x+4)/(x^2+9) with respect to x	$\int \frac{2 x + 4}{x^{2} + 9} d x$
83940	Find the Integral	(10t^-3+12t^-9+4t^3)dt	$(10 t^{- 3} + 12 t^{- 9} + 4 t^{3}) d t$
83941	Find the Derivative - d/dx	(2x^2)/2	$\frac{2 x^{2}}{2}$
83942	Find the Derivative - d/dx	(8cos(x-1))	$(8 \cos (x - 1))$
83943	Evaluate the Limit	limit as x approaches 0 from the right of x natural log of 3x+4x^2	$lim_{x \to 0^{+}} x \ln (3 x + 4 x^{2})$
83944	Find the Antiderivative	4e^x+x	$4 e^{x} + x$
83945	Find dy/dx	-4x^2=-y^2-y^3	$- 4 x^{2} = - y^{2} - y^{3}$
83946	Find the Antiderivative	f(x)=1/( square root of 42-3x)	$f (x) = \frac{1}{\sqrt{42 - 3 x}}$
83947	Find the Antiderivative	f(x)=9/(cos(x)^2)-3sin(x)	$f (x) = \frac{9}{\cos^{2} (x)} - 3 \sin (x)$
83948	Evaluate the Limit	limit as x approaches -3 of (x^2+3x)/(4(x+3))	$lim_{x \to - 3} \frac{x^{2} + 3 x}{4 (x + 3)}$
83949	Integrate Using u-Substitution	integral of x^(1/3)(x^(4/3)+9)^8 with respect to x	$\int x^{\frac{1}{3}} {(x^{\frac{4}{3}} + 9)}^{8} d x$
83950	Eliminate the Parameter	x=2+4t and y=-1+6t	$x = 2 + 4 t$ and $y = - 1 + 6 t$
83951	Find dy/dx	-3=xy-y	$- 3 = x y - y$
83952	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (4x^2)/(e^(4x)-4x-1)	$lim_{x \to 0} \frac{4 x^{2}}{e^{4 x} - 4 x - 1}$
83953	Find dy/dx	(x^2+y^2-1)^3-x^2y^3=0	${(x^{2} + y^{2} - 1)}^{3} - x^{2} y^{3} = 0$
83954	Evaluate the Limit	limit as t approaches 0 of (sin(t))/( natural log of 2e^t-1)	$lim_{t \to 0} \frac{\sin (t)}{\ln (2 e^{t} - 1)}$
83955	Evaluate the Limit	limit as x approaches infinity of (yx+6)/(2x-7)=4	$lim_{x \to \infty} \frac{y x + 6}{2 x - 7} = 4$
83956	Find the Integral	\|x-1\|	$\| x - 1 \|$
83957	Find the Derivative - d/dx	sin(2x)-tan(x)-x	$\sin (2 x) - \tan (x) - x$
83958	Find the Absolute Max and Min over the Interval	x^3-3x^2+12 , [-2,4]	$x^{3} - 3 x^{2} + 12$ , $[- 2, 4]$
83959	Find dy/dx	e^y=(x^2)/y	$e^{y} = \frac{x^{2}}{y}$
83960	Find the Derivative - d/dx	natural log of e^x+x	$\ln (e^{x} + x)$
83961	Evaluate the Integral	integral from 1 to e of 1/(x square root of natural log of x) with respect to x	$\int_{1}^{e} \frac{1}{x \sqrt{\ln (x)}} d x$
83962	Evaluate the Integral	integral from 1 to 4 of (5x^2+ square root of x) with respect to x	$\int_{1}^{4} (5 x^{2} + \sqrt{x}) d x$
83963	Find the Antiderivative	(2/e)^x	${(\frac{2}{e})}^{x}$
83964	Find dy/dx	y=tan(xsin(x))	$y = \tan (x \sin (x))$
83965	Find the Antiderivative	e^(2x)+2/x	$e^{2 x} + \frac{2}{x}$
83966	Evaluate the Limit	limit as x approaches 1 of x^2sin(pix^2)	$lim_{x \to 1} x^{2} \sin (π x^{2})$
83967	Find the Antiderivative	(2x^4+4x^3-x)/(x^3)	$\frac{2 x^{4} + 4 x^{3} - x}{x^{3}}$
83968	Find the Second Derivative	square root of 2x-x^2	$\sqrt{2 x - x^{2}}$
83969	Find the Derivative - d/dx	y=e^(2x)-xcos(xy)	$y = e^{2 x} - x \cos (x y)$
83970	Determine if Continuous	h(x)=x^2+k^2,0<=x<=2; (2x+4)/(x-1),x>2	$h (x) = {\begin{cases} x^{2} + k^{2}, 0 \leq x \leq 2 \\ \frac{2 x + 4}{x - 1}, x > 2 \end{cases}$
83971	Evaluate the Integral	integral from 0 to square root of 3/2 of 1/( square root of 1-r^2) with respect to r	$\int_{0}^{\sqrt{\frac{3}{2}}} \frac{1}{\sqrt{1 - r^{2}}} d r$
83972	Find the Derivative - d/dx	y=(csc(x/2)^2)/(3x+4)	$y = \frac{\csc^{2} (\frac{x}{2})}{3 x + 4}$
83973	Evaluate the Limit	limit as t approaches 0 of t/(e^t-1)	$lim_{t \to 0} \frac{t}{e^{t} - 1}$
83974	Find Where Increasing/Decreasing	y=x/(x^2+1)	$y = \frac{x}{x^{2} + 1}$
83975	Evaluate the Integral	integral of (sin( square root of 3x))/( square root of 3x) with respect to x	$\int \frac{\sin (\sqrt{3 x})}{\sqrt{3 x}} d x$
83976	Evaluate the Integral	integral of (4+3x^3-2 square root of x) with respect to x	$\int (4 + 3 x^{3} - 2 \sqrt{x}) d x$
83977	Find the Antiderivative	natural log of 1-x	$\ln (1 - x)$
83978	Integrate By Parts	integral of xcsc(x)^2 with respect to x	$\int x \csc^{2} (x) d x$
83979	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (x^2-1)/(sin(pix))	$lim_{x \to 1} \frac{x^{2} - 1}{\sin (π x)}$
83980	Find dy/dx	y^2=2+xy	$y^{2} = 2 + x y$
83981	Find dy/dx	y=arcsin(tan(x^3))	$y = \arcsin (\tan (x^{3}))$
83982	Find the Antiderivative	f(t)=(2t-4+4 square root of t)/( square root of t)	$f (t) = \frac{2 t - 4 + 4 \sqrt{t}}{\sqrt{t}}$
83983	Evaluate the Integral	integral of (x^4+x^3-x^2) with respect to x	$\int (x^{4} + x^{3} - x^{2}) d x$
83984	Find the Antiderivative	f(x)=e^(3x+1)	$f (x) = e^{3 x + 1}$
83985	Find the Derivative - d/da	x^4+4x^by+ax^2y^2+4xy^3+y^4	$x^{4} + 4 x^{b} y + a x^{2} y^{2} + 4 x y^{3} + y^{4}$
83986	Evaluate the Integral	integral of (7u^(3/2)+2u^(1/2)) with respect to u	$\int (7 u^{\frac{3}{2}} + 2 u^{\frac{1}{2}}) d u$
83987	Evaluate the Summation	5 sum from i=0 to 3 of i^2-4i	$5 \sum_{i = 0}^{3} i^{2} - 4 i$
83988	Find the Antiderivative	f(x)=4+sin(x)	$f (x) = 4 + \sin (x)$
83989	Find the Derivative - d/dx	natural log of 3xe^(5x)	$\ln (3 x) e^{5 x}$
83990	Evaluate the Integral	integral of (20x^4-9x^3+10x^2)/x with respect to x	$\int \frac{20 x^{4} - 9 x^{3} + 10 x^{2}}{x} d x$
83991	Find the Domain and Range	f(x)=1-x if x<=-1; 2 if -1=1	$f (x) = {\begin{cases} 1 - x & x \leq - 1 \\ 2 & - 1 = 1 \end{cases}$
83992	Integrate Using u-Substitution	integral of (x^2+1)^2 with respect to x	$\int {(x^{2} + 1)}^{2} d x$
83993	Evaluate from the Right	limit as x approaches 2 of 1+3x	$lim_{x \to 2} 1 + 3 x$
83994	Find the Derivative - d/dx	natural log of ( square root of 4+x^2)/x	$\ln (\frac{\sqrt{4 + x^{2}}}{x})$
83995	Find the Area Between the Curves	y=tan(5x) , y=2sin(5x) , -pi/15<=x<=pi/15	$y = \tan (5 x)$ , $y = 2 \sin (5 x)$ , $- \frac{π}{15} \leq x \leq \frac{π}{15}$
83996	Find dy/dx	y=(x^2-4)/(5x-3)	$y = \frac{x^{2} - 4}{5 x - 3}$
83997	Find the Derivative - d/dx	cosh(x)^2	$\cosh^{2} (x)$
83998	Find dy/dx	y=-2x^4 square root of 4x+5	$y = - 2 x^{4} \sqrt{4 x + 5}$
83999	Find dy/dx	y=e^(-x/2)	$y = e^{- \frac{x}{2}}$
84000	Evaluate the Integral	integral of (1-x-y)^2 with respect to y	$\int {(1 - x - y)}^{2} d y$