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Popular Calculus Problems

integral of sin(2x)sin(4x)	\int\:\sin(2x)\sin(4x)dx
(\partial)/(\partial x)(xsqrt(1+y^7))	\frac{\partial\:}{\partial\:x}(x\sqrt{1+y^{7}})
derivative of \sqrt[3]{x^2}+4sqrt(x^3)	\frac{d}{dx}(\sqrt[3]{x^{2}}+4\sqrt{x^{3}})
taylor sin(1/x)	taylor\:\sin(\frac{1}{x})
limit as x approaches 0+of (ln(x))/(sqrt(x))	\lim\:_{x\to\:0+}(\frac{\ln(x)}{\sqrt{x}})
integral of-4x^3-8x^2-4	\int\:-4x^{3}-8x^{2}-4dx
derivative of-x^2+5x	\frac{d}{dx}(-x^{2}+5x)
(\partial ^2)/(\partial x^2)(x)	\frac{\partial\:^{2}}{\partial\:x^{2}}(x)
limit as x approaches 3-of x/(x-3)	\lim\:_{x\to\:3-}(\frac{x}{x-3})
integral from 1 to infinity of 3x^{-4}	\int\:_{1}^{\infty\:}3x^{-4}dx
integral from 0 to 1 of xe^{6x}	\int\:_{0}^{1}xe^{6x}dx
integral of sqrt(y-1)	\int\:\sqrt{y-1}dy
(d^2y)/(dx^2)+(dy)/(dx)=2e^x	\frac{d^{2}y}{dx^{2}}+\frac{dy}{dx}=2e^{x}
integral of 5e^{6x}cos(e^{6x})	\int\:5e^{6x}\cos(e^{6x})dx
y^{''}+2y^'+5y=4cos(2t)e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=4\cos(2t)e^{-t}
(\partial)/(\partial x)(sin(x^2-9xy))	\frac{\partial\:}{\partial\:x}(\sin(x^{2}-9xy))
integral of 1/(cos^5(x))	\int\:\frac{1}{\cos^{5}(x)}dx
2yy^'+2=y^2+2x,y(0)=6	2yy^{\prime\:}+2=y^{2}+2x,y(0)=6
derivative of 2/(x^{1/3)}-2	derivative\:\frac{2}{x^{\frac{1}{3}}}-2
2y^'+ty=7	2y^{\prime\:}+ty=7
derivative of (3x-1/(2x+5))	\frac{d}{dx}(\frac{3x-1}{2x+5})
area y=4x^2,y^2= 1/4 x	area\:y=4x^{2},y^{2}=\frac{1}{4}x
y^{''}-x^2+y^'=0	y^{\prime\:\prime\:}-x^{2}+y^{\prime\:}=0
integral of (1-x^2)/x	\int\:\frac{1-x^{2}}{x}dx
derivative of f(x)=7^x	derivative\:f(x)=7^{x}
laplacetransform 2/3 t^3*e^{-8t}	laplacetransform\:\frac{2}{3}t^{3}\cdot\:e^{-8t}
derivative of 4/(x^2-2/x)	\frac{d}{dx}(\frac{4}{x^{2}}-\frac{2}{x})
3y^3e^xdx+e^{-x}dy=3y^3dx	3y^{3}e^{x}dx+e^{-x}dy=3y^{3}dx
derivative of ln(1-1/x)	\frac{d}{dx}(\ln(1-\frac{1}{x}))
(\partial)/(\partial x)(3y^2+20x^2y^3)	\frac{\partial\:}{\partial\:x}(3y^{2}+20x^{2}y^{3})
laplacetransform cos^2(pit)	laplacetransform\:\cos^{2}(πt)
x^2y^'+xy=y^2	x^{2}y^{\prime\:}+xy=y^{2}
limit as x approaches-1 of (x+1)*ln(x+1)	\lim\:_{x\to\:-1}((x+1)\cdot\:\ln(x+1))
inverse oflaplace 2/(s+1)+32*s/(s^2+9)	inverselaplace\:\frac{2}{s+1}+32\cdot\:\frac{s}{s^{2}+9}
tangent of f(x)=x^4,(-1,1)	tangent\:f(x)=x^{4},(-1,1)
slope of y=4x-2x^2	slope\:y=4x-2x^{2}
derivative of (ax+b^n)	\frac{d}{dx}((ax+b)^{n})
derivative of f(x)=(x^2)/2+2x+4	derivative\:f(x)=\frac{x^{2}}{2}+2x+4
f^'(x)= 9/(2sqrt(9x-5))	f^{\prime\:}(x)=\frac{9}{2\sqrt{9x-5}}
integral of 1/(x^2sqrt(25-x^2))	\int\:\frac{1}{x^{2}\sqrt{25-x^{2}}}dx
derivative of sqrt(x)*(ln(x))^2	derivative\:\sqrt{x}\cdot\:(\ln(x))^{2}
integral of sin(x)+cos(y)	\int\:\sin(x)+\cos(y)dx
integral of (sqrt(9-x^2))/((x^2))	\int\:\frac{\sqrt{9-x^{2}}}{(x^{2})}dx
integral of 2cos(t)sin(t)	\int\:2\cos(t)\sin(t)dt
integral of sqrt(4x-3)	\int\:\sqrt{4x-3}dx
derivative of (xsinh(x)/(sinh(2x)))	\frac{d}{dx}(\frac{x\sinh(x)}{\sinh(2x)})
tangent of y= 2/(sqrt(x)),(9, 2/3)	tangent\:y=\frac{2}{\sqrt{x}},(9,\frac{2}{3})
integral of (cos(x))/((cos^2(x))^{3/2)}	\int\:\frac{\cos(x)}{(\cos^{2}(x))^{\frac{3}{2}}}dx
integral of (3x-24)/(x^3-4x^2+4x)	\int\:\frac{3x-24}{x^{3}-4x^{2}+4x}dx
integral from 0 to 2 of e^{4x}	\int\:_{0}^{2}e^{4x}dx
integral of (x+5)/((x+3)(x-2)^2)	\int\:\frac{x+5}{(x+3)(x-2)^{2}}dx
limit as x approaches-4 of 3ln(9)(7-5x)	\lim\:_{x\to\:-4}(3\ln(9)(7-5x))
limit as x approaches 0 of sin(x)-e^x	\lim\:_{x\to\:0}(\sin(x)-e^{x})
(dy)/(dt)-2ty=-12t^2e^{t^2},y(0)=-1	\frac{dy}{dt}-2ty=-12t^{2}e^{t^{2}},y(0)=-1
integral of (ln(4x))^2	\int\:(\ln(4x))^{2}dx
integral from 2 to 4 of 1-(x-3)^2	\int\:_{2}^{4}1-(x-3)^{2}dx
(\partial)/(\partial x)(6q(r,t,x)^2+7r^3-8/t-q(r,t,x)t)	\frac{\partial\:}{\partial\:x}(6q(r,t,x)^{2}+7r^{3}-\frac{8}{t}-q(r,t,x)t)
yy^'+x=0	yy^{\prime\:}+x=0
derivative of x^{3/4}	derivative\:x^{\frac{3}{4}}
integral of y^2(1-2x)	\int\:y^{2}(1-2x)dy
(\partial)/(\partial x)(y(e^x-1))	\frac{\partial\:}{\partial\:x}(y(e^{x}-1))
limit as x approaches 0 of x^2+16x+25	\lim\:_{x\to\:0}(x^{2}+16x+25)
sum from k=0 to infinity of 2/(k!)	\sum\:_{k=0}^{\infty\:}\frac{2}{k!}
integral of (4x-3)^2	\int\:(4x-3)^{2}dx
limit as x approaches 0+of (ln(x))^x	\lim\:_{x\to\:0+}((\ln(x))^{x})
derivative of 1/x ln(e^x+x)	\frac{d}{dx}(\frac{1}{x}\ln(e^{x}+x))
(\partial)/(\partial x)(sin(8x)cos(2y))	\frac{\partial\:}{\partial\:x}(\sin(8x)\cos(2y))
integral from 1 to 4 of sqrt(x)*ln(x)	\int\:_{1}^{4}\sqrt{x}\cdot\:\ln(x)dx
derivative of (x^3/3+8/3-x^2+4)	\frac{d}{dx}(\frac{x^{3}}{3}+\frac{8}{3}-x^{2}+4)
y^{''}-4y^'+5y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}-4y^{\prime\:}+5y=0,y(0)=1,y^{\prime\:}(0)=0
y^'=6x	y^{\prime\:}=6x
derivative of-x^2+2x+1	\frac{d}{dx}(-x^{2}+2x+1)
(\partial)/(\partial y)(e^{x+2y})	\frac{\partial\:}{\partial\:y}(e^{x+2y})
y^'=xe^{x-y}	y^{\prime\:}=xe^{x-y}
limit as x approaches 50 of x+10	\lim\:_{x\to\:50}(x+10)
integral of (e^{-x})/(sqrt(1-e^{-2x))}	\int\:\frac{e^{-x}}{\sqrt{1-e^{-2x}}}dx
integral of (sqrt(r)+3)/(r+3)	\int\:\frac{\sqrt{r}+3}{r+3}dr
(d^4)/(dx^4)(xe^{5x}cos(2x))	\frac{d^{4}}{dx^{4}}(xe^{5x}\cos(2x))
integral from-2pi to-(5pi)/2 of 5cos(x)	\int\:_{-2π}^{-\frac{5π}{2}}5\cos(x)dx
integral of 1/(sqrt((1-u^2)^3))	\int\:\frac{1}{\sqrt{(1-u^{2})^{3}}}du
(\partial)/(\partial y)((2xy^2)/(2+x^2y^2))	\frac{\partial\:}{\partial\:y}(\frac{2xy^{2}}{2+x^{2}y^{2}})
integral of (82x+8)/((9x+1)(x-1))	\int\:\frac{82x+8}{(9x+1)(x-1)}dx
limit as x approaches+6 of x^2	\lim\:_{x\to\:+6}(x^{2})
integral of sqrt(4+9x)	\int\:\sqrt{4+9x}dx
tangent of y=(2x)/(x^2+1),(1,1)	tangent\:y=\frac{2x}{x^{2}+1},(1,1)
integral of (2x+1)/(3x^2+3x-2)	\int\:\frac{2x+1}{3x^{2}+3x-2}dx
(\partial}{\partial x}(sin(\frac{4x)/y))	\frac{\partial\:}{\partial\:x}(\sin(\frac{4x}{y}))
integral of x^2-17	\int\:x^{2}-17dx
integral of cos^8(3x)sin^3(3x)	\int\:\cos^{8}(3x)\sin^{3}(3x)dx
expand (3x-3x^2)tan(x)	expand\:(3x-3x^{2})\tan(x)
9(t+1)((dy)/(dt))-6y=18t	9(t+1)(\frac{dy}{dt})-6y=18t
derivative of (x^2-4x)/((x-2)^2)	derivative\:\frac{x^{2}-4x}{(x-2)^{2}}
integral of (2^{(18x)})/4	\int\:\frac{2^{(18x)}}{4}dx
integral of 2xsqrt(x)	\int\:2x\sqrt{x}dx
derivative of (9x^3+3x^2^4)	\frac{d}{dx}((9x^{3}+3x^{2})^{4})
-y^'-5y=-t	-y^{\prime\:}-5y=-t
(dy)/(dx)+10(tan(10x))y=cos(10x)	\frac{dy}{dx}+10(\tan(10x))y=\cos(10x)
(dy)/(dx)=4x^3sqrt(y)	\frac{dy}{dx}=4x^{3}\sqrt{y}
integral of (D(5x^2+5y^2)-1)/2	\int\:\frac{D(5x^{2}+5y^{2})-1}{2}dA
xy^'+2y=3sin(x)	xy^{\prime\:}+2y=3\sin(x)

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