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Popular Calculus Problems

limit as x approaches-infinity of 1-e^x	\lim\:_{x\to\:-\infty\:}(1-e^{x})
derivative of (x^3-8)^{2/3}	derivative\:(x^{3}-8)^{\frac{2}{3}}
d/(da)(sin(a)+sin(2a)+sin(3a))	\frac{d}{da}(\sin(a)+\sin(2a)+\sin(3a))
inverse oflaplace-(5s)/((s^2+1)^2)	inverselaplace\:-\frac{5s}{(s^{2}+1)^{2}}
integral of (x+1)(x+3)	\int\:(x+1)(x+3)dx
inverse oflaplace (-0.1s)/(s^2-9.8)	inverselaplace\:\frac{-0.1s}{s^{2}-9.8}
derivative of y= 4/3 (x+1)^{3/2}	derivative\:y=\frac{4}{3}(x+1)^{\frac{3}{2}}
integral from 0 to-0.5 of 150x	\int\:_{0}^{-0.5}150xdx
derivative of (x^2+5)^2(x-5)	derivative\:(x^{2}+5)^{2}(x-5)
integral of 6x^2+16x-10	\int\:6x^{2}+16x-10dx
(\partial)/(\partial y)(sin(pi(5x-2y)))	\frac{\partial\:}{\partial\:y}(\sin(π(5x-2y)))
integral of cosh^2(x)	\int\:\cosh^{2}(x)dx
integral of ye^{-3y}	\int\:ye^{-3y}dy
derivative of (x^2+3x^4)	\frac{d}{dx}((x^{2}+3x)^{4})
derivative of X^{1/5}	derivative\:X^{\frac{1}{5}}
integral of 2/(e^x+e^{-x)}	\int\:\frac{2}{e^{x}+e^{-x}}dx
integral of 6cos(sqrt(8x))	\int\:6\cos(\sqrt{8x})dx
derivative of 1/z	derivative\:\frac{1}{z}
integral of (3x^2-2x+5)	\int\:(3x^{2}-2x+5)dx
f(x)=-3/x	f(x)=-\frac{3}{x}
integral of (sin(2x))/(32+cos^2(x))	\int\:\frac{\sin(2x)}{32+\cos^{2}(x)}dx
(dP)/(dt)=0.16P(1-P/(1000))-30,P(0)=200	\frac{dP}{dt}=0.16P(1-\frac{P}{1000})-30,P(0)=200
derivative of 6cos(t)-2sin(t)	derivative\:6\cos(t)-2\sin(t)
slope of f(t)=t^3-27t+5	slope\:f(t)=t^{3}-27t+5
tangent of y=ln(x^4-4095),(8,0)	tangent\:y=\ln(x^{4}-4095),(8,0)
integral of-sec(x)tan(x)	\int\:-\sec(x)\tan(x)dx
derivative of ln(x+sqrt(x^2-9))	\frac{d}{dx}(\ln(x+\sqrt{x^{2}-9}))
derivative of (x+1/(x^3+x-2))	\frac{d}{dx}(\frac{x+1}{x^{3}+x-2})
derivative of xln(5x)	\frac{d}{dx}(x\ln(5x))
tangent of 3x^2-4x+6,\at x=2	tangent\:3x^{2}-4x+6,\at\:x=2
y^{''}+4y=0,y(0)=1,y(1)=0	y^{\prime\:\prime\:}+4y=0,y(0)=1,y(1)=0
d/(dt)(ae^tcos(2t)+be^tsin(2t))	\frac{d}{dt}(ae^{t}\cos(2t)+be^{t}\sin(2t))
limit as x approaches 0 of (1+x)^2-1	\lim\:_{x\to\:0}((1+x)^{2}-1)
limit as x approaches 1 of sqrt(6x^2+1)	\lim\:_{x\to\:1}(\sqrt{6x^{2}+1})
limit as x approaches 1 of \sqrt[3]{x}-1	\lim\:_{x\to\:1}(\sqrt[3]{x}-1)
integral of 1/(4+v^2)	\int\:\frac{1}{4+v^{2}}dv
f(x)=(sqrt(1-x^2))/x	f(x)=\frac{\sqrt{1-x^{2}}}{x}
derivative of y=10csc(5x^5-4x+4)	derivative\:y=10\csc(5x^{5}-4x+4)
integral of (3x^2)/((1-x)(x^2+x+1))	\int\:\frac{3x^{2}}{(1-x)(x^{2}+x+1)}dx
limit as x approaches 4 of-x^2+6x-3	\lim\:_{x\to\:4}(-x^{2}+6x-3)
sum from n=0 to infinity of x^{2n+1}	\sum\:_{n=0}^{\infty\:}x^{2n+1}
derivative of 1/(sqrt(1-2x))	\frac{d}{dx}(\frac{1}{\sqrt{1-2x}})
derivative of y=xsin(x)+2	derivative\:y=x\sin(x)+2
x^{''}-x^'-6x=6e^{3t}+2e^{-2t}	x^{\prime\:\prime\:}-x^{\prime\:}-6x=6e^{3t}+2e^{-2t}
integral of e^{kt}	\int\:e^{kt}dt
(\partial)/(\partial x)((5x^3y+4y^5)^3)	\frac{\partial\:}{\partial\:x}((5x^{3}y+4y^{5})^{3})
laplacetransform sin^2(6t)	laplacetransform\:\sin^{2}(6t)
derivative of e^{1/x}-(e^{1/x}/x)	\frac{d}{dx}(e^{\frac{1}{x}}-\frac{e^{\frac{1}{x}}}{x})
derivative of sqrt(x^3+x^5)	\frac{d}{dx}(\sqrt{x^{3}+x^{5}})
integral of x/(sqrt(2-x^2))	\int\:\frac{x}{\sqrt{2-x^{2}}}dx
(\partial)/(\partial x)((x^2)/(x^2+1))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{x^{2}+1})
((f(t))/(g(t)))'	(\frac{f(t)}{g(t)})\prime\:
derivative of sqrt(x)e^{x^2}(x^2+1^{10})	\frac{d}{dx}(\sqrt{x}e^{x^{2}}(x^{2}+1)^{10})
x(dy)/(dx)=2x^2+y,y(1)=3	x\frac{dy}{dx}=2x^{2}+y,y(1)=3
sum from n=2 to infinity of 1/(n^2+5n+6)	\sum\:_{n=2}^{\infty\:}\frac{1}{n^{2}+5n+6}
sum from n=1 to infinity of (5n)/(3n-1)	\sum\:_{n=1}^{\infty\:}\frac{5n}{3n-1}
derivative of-(2x/(x-1))	\frac{d}{dx}(-\frac{2x}{x-1})
derivative of f(x)=7(2-3x)^4	derivative\:f(x)=7(2-3x)^{4}
integral of ((x^{am}-x^n))/(sqrt(x))	\int\:\frac{(x^{am}-x^{n})}{\sqrt{x}}dx
integral of 11^x	\int\:11^{x}dx
limit as x approaches 0-of (x^2)/5-7/x	\lim\:_{x\to\:0-}(\frac{x^{2}}{5}-\frac{7}{x})
d/(dt)(1/(12sqrt(t)))	\frac{d}{dt}(\frac{1}{12\sqrt{t}})
integral of (3xsqrt(2x^2+9))/5	\int\:\frac{3x\sqrt{2x^{2}+9}}{5}dx
integral from 0 to 7 of sqrt(y+9)	\int\:_{0}^{7}\sqrt{y+9}dy
tangent of f(x)=2sin(x),\at x= pi/6	tangent\:f(x)=2\sin(x),\at\:x=\frac{π}{6}
(\partial)/(\partial x)(e^{5xyz-6})	\frac{\partial\:}{\partial\:x}(e^{5xyz-6})
integral of 1+3x^2y^2	\int\:1+3x^{2}y^{2}dy
derivative of-12	\frac{d}{dx}(-12)
(d^2)/(dx^2)((4x+3)(2x^2+7x-1))	\frac{d^{2}}{dx^{2}}((4x+3)(2x^{2}+7x-1))
taylor e^{(-x^2)/2}	taylor\:e^{\frac{-x^{2}}{2}}
integral of cosh(5x+ln(6))	\int\:\cosh(5x+\ln(6))dx
integral of (3cos(1/2 x))	\int\:(3\cos(\frac{1}{2}x))dx
slope of (-3)(0.15)	slope\:(-3)(0.15)
integral of 3((cos(x)+sin(x))/(sin(2x)))	\int\:3(\frac{\cos(x)+\sin(x)}{\sin(2x)})dx
integral from 2 to 6 of 4+2x^2	\int\:_{2}^{6}4+2x^{2}dx
integral of (10+x)^{-2}	\int\:(10+x)^{-2}dx
integral of (2x^4-x)/(x^3)	\int\:\frac{2x^{4}-x}{x^{3}}dx
integral of (x+7)^7(x+8)	\int\:(x+7)^{7}(x+8)dx
derivative of f(x)=(3x^2-x+1)/x	derivative\:f(x)=\frac{3x^{2}-x+1}{x}
derivative of 4^{ln(x})	\frac{d}{dx}(4^{\ln(x)})
integral from 0 to 1 of 2pix(15-15x)	\int\:_{0}^{1}2πx(15-15x)dx
integral of (x^4-\sqrt[3]{x})/(6sqrt(x))	\int\:\frac{x^{4}-\sqrt[3]{x}}{6\sqrt{x}}dx
integral of 1/x ln(x)	\int\:\frac{1}{x}\ln(x)dx
integral of-(t-6)^2	\int\:-(t-6)^{2}dt
d/(dy)(x^{0.5}y^{0.5})	\frac{d}{dy}(x^{0.5}y^{0.5})
derivative of x^{7/9}	derivative\:x^{\frac{7}{9}}
tangent of f(x)=x^2-7,\at x=2	tangent\:f(x)=x^{2}-7,\at\:x=2
limit as x approaches 2-of (x^2)/(x^2+4)	\lim\:_{x\to\:2-}(\frac{x^{2}}{x^{2}+4})
d/(dθ)(1+2sin(θ))	\frac{d}{dθ}(1+2\sin(θ))
derivative of sin(6x^2)	\frac{d}{dx}(\sin(6x^{2}))
integral of-(e^{-2x}*(5+2x-2y^2))	\int\:-(e^{-2x}\cdot\:(5+2x-2y^{2}))dx
4xy^'-4y=7x^4	4xy^{\prime\:}-4y=7x^{4}
integral of tan^6(x)sec^2(x)	\int\:\tan^{6}(x)\sec^{2}(x)dx
derivative of x^4+6x	derivative\:x^{4}+6x
f(x)=e^xsin(x)	f(x)=e^{x}\sin(x)
derivative of x^2sqrt(x^2+1)	\frac{d}{dx}(x^{2}\sqrt{x^{2}+1})
limit as x approaches 0-of \|(5x)/x \|	\lim\:_{x\to\:0-}(\left\|\frac{5x}{x}\right\|)
integral of 1/((x^2-4x)^{3/2)}	\int\:\frac{1}{(x^{2}-4x)^{\frac{3}{2}}}dx
integral of ((sin(31x))/(1+cos^2(31x)))	\int\:(\frac{\sin(31x)}{1+\cos^{2}(31x)})dx
derivative of e^{t+7}	derivative\:e^{t+7}

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