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Popular Calculus Problems

integral of (x^3)/(sqrt(1-x^2))	\int\:\frac{x^{3}}{\sqrt{1-x^{2}}}dx
inverse oflaplace (e^{-s})/(s^2)	inverselaplace\:\frac{e^{-s}}{s^{2}}
sum from n=0 to infinity of e^{-0.02n}	\sum\:_{n=0}^{\infty\:}e^{-0.02n}
laplacetransform (t+7)^3	laplacetransform\:(t+7)^{3}
derivative of (t-sqrt(t))/(t^{1/6)}	derivative\:\frac{t-\sqrt{t}}{t^{\frac{1}{6}}}
tangent of (2x-1)^2	tangent\:(2x-1)^{2}
derivative of ln(x^{9/2})	\frac{d}{dx}(\ln(x^{\frac{9}{2}}))
integral of (16)/((x^2-4)(x-2))	\int\:\frac{16}{(x^{2}-4)(x-2)}dx
((((dy)/(dx))-e^{-x}+5))/y =-5	\frac{((\frac{dy}{dx})-e^{-x}+5)}{y}=-5
derivative of x^{0.3}	\frac{d}{dx}(x^{0.3})
integral of 2cos^2(3x)	\int\:2\cos^{2}(3x)dx
limit as x approaches infinity of 9/2	\lim\:_{x\to\:\infty\:}(\frac{9}{2})
derivative of y=8^{4^{x^2}}	derivative\:y=8^{4^{x^{2}}}
integral of (-9x^2)/((3-3x^3)^2)	\int\:\frac{-9x^{2}}{(3-3x^{3})^{2}}dx
integral of (-x+7)/(x^2+x-6)	\int\:\frac{-x+7}{x^{2}+x-6}dx
integral of (x^2)/(x^2-4x+3)	\int\:\frac{x^{2}}{x^{2}-4x+3}dx
taylor x^{3/2},4	taylor\:x^{\frac{3}{2}},4
(\partial)/(\partial x)(-210(5x-y)^5)	\frac{\partial\:}{\partial\:x}(-210(5x-y)^{5})
derivative of 1+csqrt(1-x^2)	\frac{d}{dx}(1+c\sqrt{1-x^{2}})
slope of y=(6x)/(x^2+1)	slope\:y=\frac{6x}{x^{2}+1}
integral from-2 to 2 of 1	\int\:_{-2}^{2}1dx
derivative of tan(x^8)	derivative\:\tan(x^{8})
integral of 4sec^6(x)	\int\:4\sec^{6}(x)dx
integral of 1/(s+sqrt(2))	\int\:\frac{1}{s+\sqrt{2}}ds
slope of (-2,-5),(2,-8)	slope\:(-2,-5),(2,-8)
tangent of y=(1+5x)^{11},(0,1)	tangent\:y=(1+5x)^{11},(0,1)
integral from 4 to 8 of 1/(x^2-1)	\int\:_{4}^{8}\frac{1}{x^{2}-1}dx
derivative of-2/((1-x)^3)	derivative\:-\frac{2}{(1-x)^{3}}
integral of (x^3)/((x^2+5)^2)	\int\:\frac{x^{3}}{(x^{2}+5)^{2}}dx
integral of cos^3(x/(15))	\int\:\cos^{3}(\frac{x}{15})dx
integral of (10)/((x-1)(x^2+9))	\int\:\frac{10}{(x-1)(x^{2}+9)}dx
maclaurin cos(pi)(x),0	maclaurin\:\cos(π)(x),0
derivative of 120x^3-240x^2+120x	\frac{d}{dx}(120x^{3}-240x^{2}+120x)
integral of 36x	\int\:36xdx
integral of cos(x)+1/5 x	\int\:\cos(x)+\frac{1}{5}xdx
derivative of sqrt(7x+1)	derivative\:\sqrt{7x+1}
integral from 2 to 5 of 8x^7	\int\:_{2}^{5}8x^{7}dx
integral from 1 to 6 of 3/(x^2)	\int\:_{1}^{6}\frac{3}{x^{2}}dx
area y=-1/5 x^2-6/5 x+7/5 ,(-5,5)	area\:y=-\frac{1}{5}x^{2}-\frac{6}{5}x+\frac{7}{5},(-5,5)
integral of e^x*sin(2x)	\int\:e^{x}\cdot\:\sin(2x)dx
derivative of \sqrt[3]{5x}+4x^{1/2}-3x	\frac{d}{dx}(\sqrt[3]{5x}+4x^{\frac{1}{2}}-3x)
x^2(dy)/(dx)-2xy=6y^4,y(1)= 1/5	x^{2}\frac{dy}{dx}-2xy=6y^{4},y(1)=\frac{1}{5}
derivative of 2xln(4x^2)	\frac{d}{dx}(2x\ln(4x^{2}))
integral of (60)/(2x+5)-5	\int\:\frac{60}{2x+5}-5dx
integral of cot(x)(-8sin(x)-10csc(x))	\int\:\cot(x)(-8\sin(x)-10\csc(x))dx
y^2+x^2y^'=0	y^{2}+x^{2}y^{\prime\:}=0
integral of x(x+2)^{-3/2}	\int\:x(x+2)^{-\frac{3}{2}}dx
integral of e^{cos(4x)}sin(4x)	\int\:e^{\cos(4x)}\sin(4x)dx
derivative of 5/(r^3)	derivative\:\frac{5}{r^{3}}
derivative of e^{x+1}-3e^x+2e^{x^3}	\frac{d}{dx}(e^{x+1}-3e^{x}+2e^{x^{3}})
t^2y^{''}+6ty^'+6y=0	t^{2}y^{\prime\:\prime\:}+6ty^{\prime\:}+6y=0
2xy^2+4=2(3-x^2y)y^'	2xy^{2}+4=2(3-x^{2}y)y^{\prime\:}
integral of 1/4 cos(2x)	\int\:\frac{1}{4}\cos(2x)dx
integral of x^5ln\|x\|	\int\:x^{5}\ln\left\|x\right\|dx
(\partial)/(\partial y)(sqrt(1+x^2+y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{1+x^{2}+y^{2}})
integral of (3x^2+2)	\int\:(3x^{2}+2)dx
integral from 0 to 1 of 6x^2(3-5x^3)^3	\int\:_{0}^{1}6x^{2}(3-5x^{3})^{3}dx
area-1/2 x^2-5/2 x-2,[-2,7]	area\:-\frac{1}{2}x^{2}-\frac{5}{2}x-2,[-2,7]
integral of 1/(xInx)	\int\:\frac{1}{xInx}dx
derivative of x^2-6x+11	\frac{d}{dx}(x^{2}-6x+11)
sum from n=0 to infinity of 1/(n!)	\sum\:_{n=0}^{\infty\:}\frac{1}{n!}
integral of (x^{1/4})	\int\:(x^{\frac{1}{4}})dx
integral from 0 to 3 of 5	\int\:_{0}^{3}5dx
derivative of 4/(sqrt(3x+9))	derivative\:\frac{4}{\sqrt{3x+9}}
integral of 1/(sinh^2(x)+cosh^2(x))	\int\:\frac{1}{\sinh^{2}(x)+\cosh^{2}(x)}dx
integral of ((ln(x))^{23})/x	\int\:\frac{(\ln(x))^{23}}{x}dx
integral of sin(x)cos(xn)	\int\:\sin(x)\cos(xn)dx
(\partial)/(\partial x)(2*ln(x)+y)	\frac{\partial\:}{\partial\:x}(2\cdot\:\ln(x)+y)
derivative of 2x^2e^{-x}	\frac{d}{dx}(2x^{2}e^{-x})
integral of 2x^3cos(x^2)	\int\:2x^{3}\cos(x^{2})dx
integral of 8cos(sqrt(6x))	\int\:8\cos(\sqrt{6x})dx
limit as x approaches 0 of (x^2)/(x^2)	\lim\:_{x\to\:0}(\frac{x^{2}}{x^{2}})
(\partial)/(\partial y)(sqrt(x^2-y))	\frac{\partial\:}{\partial\:y}(\sqrt{x^{2}-y})
integral of e^{x^2+1}2x	\int\:e^{x^{2}+1}2xdx
(dy)/(dx)(1/(x^8))-15y=12	\frac{dy}{dx}(\frac{1}{x^{8}})-15y=12
integral of 4+6x+24x^2	\int\:4+6x+24x^{2}dx
sum from n=1 to infinity of (n^7)/(6^n)	\sum\:_{n=1}^{\infty\:}\frac{n^{7}}{6^{n}}
integral of ((sqrt(x^2-49)))/(x^3)	\int\:\frac{(\sqrt{x^{2}-49})}{x^{3}}dx
taylor ln(1-2y)	taylor\:\ln(1-2y)
(\partial)/(\partial x)(2x+2xy)	\frac{\partial\:}{\partial\:x}(2x+2xy)
(x+2y)dx+(2x+y)dy=0	(x+2y)dx+(2x+y)dy=0
integral of (x^2+3)^5	\int\:(x^{2}+3)^{5}dx
integral of 42sec^4(x)	\int\:42\sec^{4}(x)dx
area x^2,0,2	area\:x^{2},0,2
integral of x 1/(sqrt(1-x^2))	\int\:x\frac{1}{\sqrt{1-x^{2}}}dx
derivative of 10cos^3(x)	\frac{d}{dx}(10\cos^{3}(x))
derivative of f(x)=sin(x)+3/4 cot(x)	derivative\:f(x)=\sin(x)+\frac{3}{4}\cot(x)
derivative of 1/(x^{-9)}	derivative\:\frac{1}{x^{-9}}
derivative of (1+7/x ^5)	\frac{d}{dx}((1+\frac{7}{x})^{5})
derivative of y=ln(sqrt(x^2-9))	derivative\:y=\ln(\sqrt{x^{2}-9})
limit as x approaches-3 of sqrt(5x^2+2x)	\lim\:_{x\to\:-3}(\sqrt{5x^{2}+2x})
integral of (1+x)/(1-\sqrt[3]{x)}	\int\:\frac{1+x}{1-\sqrt[3]{x}}dx
limit as x approaches 3 of (x-2)/(x-3)	\lim\:_{x\to\:3}(\frac{x-2}{x-3})
integral of 3/(4(4-3x)^7)	\int\:\frac{3}{4(4-3x)^{7}}dx
4y^{''}+9y=0	4y^{\prime\:\prime\:}+9y=0
integral of (4x^3)/(x^4+7)	\int\:\frac{4x^{3}}{x^{4}+7}dx
derivative of f(x)=2x^2+5x	derivative\:f(x)=2x^{2}+5x
integral of 2t	\int\:2tdt
area-x^2+4x+1,x+1	area\:-x^{2}+4x+1,x+1
integral of ((y-3))/y	\int\:\frac{(y-3)}{y}dy

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