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Popular Calculus Problems

integral of e^tt^2	\int\:e^{t}t^{2}dt
derivative of sqrt(cos(e^{x^3sin(x))})	\frac{d}{dx}(\sqrt{\cos(e^{x^{3}\sin(x)})})
(\partial)/(\partial x)(x-xy)	\frac{\partial\:}{\partial\:x}(x-xy)
derivative of-16cos(4x)	\frac{d}{dx}(-16\cos(4x))
derivative of sqrt(x)+4/(sqrt(x)+4)	\frac{d}{dx}(\sqrt{x}+\frac{4}{\sqrt{x}}+4)
integral of (sqrt(25+x^2))/x	\int\:\frac{\sqrt{25+x^{2}}}{x}dx
(\partial)/(\partial y)(xsqrt(1+y^7))	\frac{\partial\:}{\partial\:y}(x\sqrt{1+y^{7}})
tangent of f(x)=(6x)/(x+2),\at x=4	tangent\:f(x)=\frac{6x}{x+2},\at\:x=4
y^{''}-4y^'+4y=e^{2x}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=e^{2x}
(5y-2x)dy-2ydx=0	(5y-2x)dy-2ydx=0
(\partial)/(\partial x)((3x-5y)/(3x+5y))	\frac{\partial\:}{\partial\:x}(\frac{3x-5y}{3x+5y})
integral of sin(8x)	\int\:\sin(8x)dx
(\partial)/(\partial y)(e^{xy}+2x-5y)	\frac{\partial\:}{\partial\:y}(e^{xy}+2x-5y)
tangent of y=2x^3-5x+1,(1,-2)	tangent\:y=2x^{3}-5x+1,(1,-2)
integral of xsqrt(1-x^2)	\int\:x\sqrt{1-x^{2}}dx
integral of (x+2)/(x^2+25)	\int\:\frac{x+2}{x^{2}+25}dx
tangent of f(x)=(10x)/(1+x^2),(3,3)	tangent\:f(x)=\frac{10x}{1+x^{2}},(3,3)
x^5+y^4sqrt(x^6+5)y^'=0	x^{5}+y^{4}\sqrt{x^{6}+5}y^{\prime\:}=0
slope of (-5)(7.8)	slope\:(-5)(7.8)
limit as x approaches-infinity of 0.5^x	\lim\:_{x\to\:-\infty\:}(0.5^{x})
integral of ((x^3+3x))/(x^2+1)	\int\:\frac{(x^{3}+3x)}{x^{2}+1}dx
y^'=r(1-y/k)	y^{\prime\:}=r(1-\frac{y}{k})
derivative of (13)/(x^4)	derivative\:\frac{13}{x^{4}}
limit as x approaches+1+of ln(3x^2-x-2)	\lim\:_{x\to\:+1+}(\ln(3x^{2}-x-2))
derivative of y=(5x)/(e^x)	derivative\:y=\frac{5x}{e^{x}}
integral of 3ln(2x+1)	\int\:3\ln(2x+1)dx
integral of (sin(7/x))/(x^2)	\int\:\frac{\sin(\frac{7}{x})}{x^{2}}dx
derivative of x^3+3x^2+4	\frac{d}{dx}(x^{3}+3x^{2}+4)
derivative of xe^{-x}-e^{-3}	\frac{d}{dx}(xe^{-x}-e^{-3})
limit as x approaches infinity of 20^x	\lim\:_{x\to\:\infty\:}(20^{x})
integral of 1/2 x+2/3 x^2	\int\:\frac{1}{2}x+\frac{2}{3}x^{2}dx
integral of 4/(x+1)	\int\:\frac{4}{x+1}dx
integral of (2e^x)/(3e^x+1)	\int\:\frac{2e^{x}}{3e^{x}+1}dx
limit as x approaches 2+of x+2	\lim\:_{x\to\:2+}(x+2)
integral of tan^3(3x)sec^5(3x)	\int\:\tan^{3}(3x)\sec^{5}(3x)dx
(\partial}{\partial x}(\frac{x+z)/w)	\frac{\partial\:}{\partial\:x}(\frac{x+z}{w})
derivative of (x^2+1/2 x-4(-x+2))	\frac{d}{dx}((x^{2}+\frac{1}{2}x-4)(-x+2))
integral of csc^2(x/4)	\int\:\csc^{2}(\frac{x}{4})dx
y= x/3 (2x+1)^3	y=\frac{x}{3}(2x+1)^{3}
integral of (e^{3sin(x)})/(sec(x))	\int\:\frac{e^{3\sin(x)}}{\sec(x)}dx
derivative of f(x)=x^{2x}	derivative\:f(x)=x^{2x}
integral of (-ln(x))/x	\int\:\frac{-\ln(x)}{x}dx
derivative of y=ce^x	derivative\:y=ce^{x}
integral of 1/(cot(y))	\int\:\frac{1}{\cot(y)}dy
limit as x approaches 0-of x^2-1	\lim\:_{x\to\:0-}(x^{2}-1)
integral of (x^2-3x+2)/(x-1)	\int\:\frac{x^{2}-3x+2}{x-1}dx
integral of (x^2-3x-7)/((2x+3)(x+1)^2)	\int\:\frac{x^{2}-3x-7}{(2x+3)(x+1)^{2}}dx
derivative of (x^2/(sqrt(x^4+1)))	\frac{d}{dx}(\frac{x^{2}}{\sqrt{x^{4}+1}})
(dy)/(dx)=2y-1	\frac{dy}{dx}=2y-1
x^2(dy)/(dx)+y^2=xy	x^{2}\frac{dy}{dx}+y^{2}=xy
integral of cot^2(x)csc(x)	\int\:\cot^{2}(x)\csc(x)dx
(\partial)/(\partial x)(-e^{2y}cos(2x)*2)	\frac{\partial\:}{\partial\:x}(-e^{2y}\cos(2x)\cdot\:2)
area y=x^4-x^2,y^2=x^2	area\:y=x^{4}-x^{2},y^{2}=x^{2}
y^{''}-2y^'+53/4 y=0	y^{\prime\:\prime\:}-2y^{\prime\:}+\frac{53}{4}y=0
limit as x approaches 0-of (cos(x))/x	\lim\:_{x\to\:0-}(\frac{\cos(x)}{x})
(dy)/(dx)=((2x+sec^2(x)))/(2y)	\frac{dy}{dx}=\frac{(2x+\sec^{2}(x))}{2y}
limit as x approaches 2+of (x-13)/(-x+2)	\lim\:_{x\to\:2+}(\frac{x-13}{-x+2})
derivative of (t+1)^{2/3}(2t^2-1)^3	derivative\:(t+1)^{\frac{2}{3}}(2t^{2}-1)^{3}
integral of (3^{2x}+3^{4x})^2	\int\:(3^{2x}+3^{4x})^{2}dx
derivative of sqrt(17x^2+9)	\frac{d}{dx}(\sqrt{17x^{2}+9})
limit as x approaches 10 of 2f(x)	\lim\:_{x\to\:10}(2f(x))
2y^{''}+y^'-y=x+5,y(0)=1,y^'(0)=0	2y^{\prime\:\prime\:}+y^{\prime\:}-y=x+5,y(0)=1,y^{\prime\:}(0)=0
derivative of 1/(5x^4)	\frac{d}{dx}(\frac{1}{5x^{4}})
derivative of e^{-ln(x})	\frac{d}{dx}(e^{-\ln(x)})
integral from-1 to 3 of (x^3+2x-5)	\int\:_{-1}^{3}(x^{3}+2x-5)dx
limit as x approaches 4 of sqrt(x-5)	\lim\:_{x\to\:4}(\sqrt{x-5})
integral of-2x^4	\int\:-2x^{4}dx
area y=x^2-2x,y=-x^2+6x	area\:y=x^{2}-2x,y=-x^{2}+6x
limit as x approaches 3 of-(2/(x-3))	\lim\:_{x\to\:3}(-(\frac{2}{x-3}))
derivative of f(x)=7e^{(3x^2-2x+7)}	derivative\:f(x)=7e^{(3x^{2}-2x+7)}
y^'= 1/(sec^2(x))	y^{\prime\:}=\frac{1}{\sec^{2}(x)}
d/(d{x)}({x}^2+{y}^2+{z}^2)	\frac{d}{d{x}}({x}^{2}+{y}^{2}+{z}^{2})
area y=cos(x),y=2-cos(x),0<= x<= 2pi	area\:y=\cos(x),y=2-\cos(x),0\le\:x\le\:2π
d/(dy)(5x+4y)	\frac{d}{dy}(5x+4y)
integral from-1 to 4 of (2x+4)^2	\int\:_{-1}^{4}(2x+4)^{2}dx
derivative of ln((2x/3))	\frac{d}{dx}(\ln(\frac{2x}{3}))
derivative of 1/((1-x^4))	\frac{d}{dx}(\frac{1}{(1-x)^{4}})
integral of (cos(x))/((sin(x))^2)	\int\:\frac{\cos(x)}{(\sin(x))^{2}}dx
derivative of sin^2(2x^3+2x^2)	\frac{d}{dx}(\sin^{2}(2x^{3}+2x^{2}))
derivative of x^2-7x+10	\frac{d}{dx}(x^{2}-7x+10)
(\partial)/(\partial x)(ln(5x+y^3))	\frac{\partial\:}{\partial\:x}(\ln(5x+y^{3}))
(dy)/(dx)=y(1-0.0008y)	\frac{dy}{dx}=y(1-0.0008y)
integral of (x^3+4)/(x+2)	\int\:\frac{x^{3}+4}{x+2}dx
integral of (1-x)/x	\int\:\frac{1-x}{x}dx
integral of x^2(2x^3-5)^4	\int\:x^{2}(2x^{3}-5)^{4}dx
y^'= 5/y	y^{\prime\:}=\frac{5}{y}
(d^3)/(dx^3)(sqrt(2t+8))	\frac{d^{3}}{dx^{3}}(\sqrt{2t+8})
laplacetransform tsin(2t)	laplacetransform\:t\sin(2t)
d/(dh)((n^2h^2)/(8mL^2))	\frac{d}{dh}(\frac{n^{2}h^{2}}{8mL^{2}})
t^2y^{''}+19ty^'+145y=0	t^{2}y^{\prime\:\prime\:}+19ty^{\prime\:}+145y=0
integral of x/(sqrt(x^2+8))	\int\:\frac{x}{\sqrt{x^{2}+8}}dx
derivative of x^8arctan(x^3)	\frac{d}{dx}(x^{8}\arctan(x^{3}))
y^'=k(y-70)	y^{\prime\:}=k(y-70)
integral of (ln(sqrt(8x)))/x	\int\:\frac{\ln(\sqrt{8x})}{x}dx
(\partial)/(\partial z)(e^{yz})	\frac{\partial\:}{\partial\:z}(e^{yz})
derivative of y=ln((x-1)/(x+3))-x	derivative\:y=\ln(\frac{x-1}{x+3})-x
limit as x approaches c of 13/3+2/3	\lim\:_{x\to\:c}(\frac{13}{3}+\frac{2}{3})
inverse oflaplace (s+1)/(s^2)	inverselaplace\:\frac{s+1}{s^{2}}
area 7x-x^2,2x,(5,10)	area\:7x-x^{2},2x,(5,10)
integral of (5x+3)/(x^2+2x-3)	\int\:\frac{5x+3}{x^{2}+2x-3}dx

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