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Popular Calculus Problems

integral of sin(8pix)	\int\:\sin(8πx)dx
integral of 1/(2x^{1/2)}	\int\:\frac{1}{2x^{\frac{1}{2}}}dx
(\partial)/(\partial r)(1/r)	\frac{\partial\:}{\partial\:r}(\frac{1}{r})
derivative of f(x)=x^3cos(3x)	derivative\:f(x)=x^{3}\cos(3x)
tangent of 4x^3-12x^2	tangent\:4x^{3}-12x^{2}
(\partial)/(\partial x)(x^4y^4+8x^9y)	\frac{\partial\:}{\partial\:x}(x^{4}y^{4}+8x^{9}y)
integral of x-1/x	\int\:x-\frac{1}{x}dx
tangent of y=(e^{-x})/(x+1)	tangent\:y=\frac{e^{-x}}{x+1}
integral of 1/(x^2+3x+1)	\int\:\frac{1}{x^{2}+3x+1}dx
f^'(x)= 2/(sqrt(x))	f^{\prime\:}(x)=\frac{2}{\sqrt{x}}
slope of-2x^5+10x^3	slope\:-2x^{5}+10x^{3}
integral of (e^x)/(e^{2x)+4e^x+4}	\int\:\frac{e^{x}}{e^{2x}+4e^{x}+4}dx
derivative of cos((1-e^{2x})/(1+e^{2x)})	derivative\:\cos(\frac{1-e^{2x}}{1+e^{2x}})
integral from 6 to 7 of (tsqrt(t-6))	\int\:_{6}^{7}(t\sqrt{t-6})dt
derivative of 3x^2+2y^2	\frac{d}{dx}(3x^{2}+2y^{2})
y^'=3(y+1)	y^{\prime\:}=3(y+1)
derivative of (cos(x))/(sin(x))	derivative\:\frac{\cos(x)}{\sin(x)}
area y=10x^3,y=10x^2	area\:y=10x^{3},y=10x^{2}
derivative of sec(2ln(x))	\frac{d}{dx}(\sec(2\ln(x)))
integral of 1/(2sqrt(x^3))	\int\:\frac{1}{2\sqrt{x^{3}}}dx
x(dy)/(dx)=2	x\frac{dy}{dx}=2
derivative of (91t)/(99t-91)	derivative\:\frac{91t}{99t-91}
derivative of 2xe^{2x}+e^{2x}	\frac{d}{dx}(2xe^{2x}+e^{2x})
integral of 1/(1-sin(z))	\int\:\frac{1}{1-\sin(z)}dz
limit as x approaches 0 of ((x+3))/x	\lim\:_{x\to\:0}(\frac{(x+3)}{x})
integral of sqrt(1+e^{-2x)}	\int\:\sqrt{1+e^{-2x}}dx
derivative of a(sin(x+xcos(x)))	\frac{d}{dx}(a(\sin(x)+x\cos(x)))
taylor ln(x),e	taylor\:\ln(x),e
integral of 3cos^5(3x)	\int\:3\cos^{5}(3x)dx
(y-x)dx+(x+y)dy=0	(y-x)dx+(x+y)dy=0
integral of (e^{2x})/(e^x+4)	\int\:\frac{e^{2x}}{e^{x}+4}dx
derivative of ln^3(5x)	\frac{d}{dx}(\ln^{3}(5x))
(\partial)/(\partial y)(2xyz^{-1})	\frac{\partial\:}{\partial\:y}(2xyz^{-1})
y^'=e^{5y+8x}	y^{\prime\:}=e^{5y+8x}
integral of 1/(e^{3x)}	\int\:\frac{1}{e^{3x}}dx
ydx-xdy+xydy=0	ydx-xdy+xydy=0
sum from n=0 to infinity of 2/(n(n+2))	\sum\:_{n=0}^{\infty\:}\frac{2}{n(n+2)}
integral of (ln(x^{49}))/x	\int\:\frac{\ln(x^{49})}{x}dx
(\partial)/(\partial x)(e^{(xy)^{1/2}})	\frac{\partial\:}{\partial\:x}(e^{(xy)^{\frac{1}{2}}})
integral of yln(x)	\int\:y\ln(x)dx
derivative of y= 5/(6x^5)	derivative\:y=\frac{5}{6x^{5}}
limit as x approaches 9 of 6x+\|x-9\|	\lim\:_{x\to\:9}(6x+\left\|x-9\right\|)
(dx)/(dy)=5(40-x)	\frac{dx}{dy}=5(40-x)
derivative of (x^2/(x^2+16))	\frac{d}{dx}(\frac{x^{2}}{x^{2}+16})
y^{''}-y=x^2-3x	y^{\prime\:\prime\:}-y=x^{2}-3x
derivative of f(x)= 1/(4x)	derivative\:f(x)=\frac{1}{4x}
derivative of x^3e^{3x}	\frac{d}{dx}(x^{3}e^{3x})
maclaurin 20e^{-x}	maclaurin\:20e^{-x}
derivative of 3e^{-x}*tan(3x)	\frac{d}{dx}(3e^{-x}\cdot\:\tan(3x))
integral of ((ln(x))/(x^3))	\int\:(\frac{\ln(x)}{x^{3}})dx
integral from 0 to 1 of x/(e^x)	\int\:_{0}^{1}\frac{x}{e^{x}}dx
(dx)/(dt)=x^2+1/49	\frac{dx}{dt}=x^{2}+\frac{1}{49}
(\partial)/(\partial x)(ln(xy)+xe^y)	\frac{\partial\:}{\partial\:x}(\ln(xy)+xe^{y})
derivative of 3z^2e^z	derivative\:3z^{2}e^{z}
integral of (2x)/(sqrt(u))	\int\:\frac{2x}{\sqrt{u}}
limit as t approaches 1 of t^{1/(t-1)}	\lim\:_{t\to\:1}(t^{\frac{1}{t-1}})
integral of (4sin(x)+5cos(x))	\int\:(4\sin(x)+5\cos(x))dx
simplify 2sqrt(x^3)+2/(sqrt(x^3))	simplify\:2\sqrt{x^{3}}+\frac{2}{\sqrt{x^{3}}}
integral of 1/(x^2-16)	\int\:\frac{1}{x^{2}-16}dx
integral of (3x^2+4x^3)/(x^3+x^4)	\int\:\frac{3x^{2}+4x^{3}}{x^{3}+x^{4}}dx
integral of 2/(10+x)	\int\:\frac{2}{10+x}dx
derivative of f(x)= 2/(3x+5)	derivative\:f(x)=\frac{2}{3x+5}
area y=3sqrt(x),y=(3x)/2	area\:y=3\sqrt{x},y=\frac{3x}{2}
derivative of-tan^2(x)	\frac{d}{dx}(-\tan^{2}(x))
inverse oflaplace 4x-3	inverselaplace\:4x-3
(\partial)/(\partial x)(9e^{x-y})	\frac{\partial\:}{\partial\:x}(9e^{x-y})
sum from n=2 to infinity of 4/(7^n)	\sum\:_{n=2}^{\infty\:}\frac{4}{7^{n}}
derivative of f(x)=a^5+cos^5(x)	derivative\:f(x)=a^{5}+\cos^{5}(x)
tangent of f(x)=x^2-3x,\at x=2	tangent\:f(x)=x^{2}-3x,\at\:x=2
tangent of y=(6x)/(x^2+1),(1,1)	tangent\:y=\frac{6x}{x^{2}+1},(1,1)
derivative of sin(xsin(x))	\frac{d}{dx}(\sin(x)\sin(x))
derivative of x^3-2x+7	\frac{d}{dx}(x^{3}-2x+7)
derivative of cos(ln(x)-sin(ln(x)))	\frac{d}{dx}(\cos(\ln(x))-\sin(\ln(x)))
d/(dy)(2y^3+1/(24y))	\frac{d}{dy}(2y^{3}+\frac{1}{24y})
derivative of 3x^2+5x	\frac{d}{dx}(3x^{2}+5x)
limit as x approaches 1+of x^{6/(1-x)}	\lim\:_{x\to\:1+}(x^{\frac{6}{1-x}})
derivative of ((x-3(x^2+3x+9))/(x^3))	\frac{d}{dx}(\frac{(x-3)(x^{2}+3x+9)}{x^{3}})
d/(dy)(3/y)	\frac{d}{dy}(\frac{3}{y})
integral of 1/(xln(x^2))	\int\:\frac{1}{x\ln(x^{2})}dx
derivative of 2x^3+x^2	\frac{d}{dx}(2x^{3}+x^{2})
y^'=-y^2	y^{\prime\:}=-y^{2}
d/(dt)(Ate^{-4t})	\frac{d}{dt}(Ate^{-4t})
integral from 2 to 3 of (12)/(sqrt(3-x))	\int\:_{2}^{3}\frac{12}{\sqrt{3-x}}dx
integral of (sqrt(x))/(x^3+1)	\int\:\frac{\sqrt{x}}{x^{3}+1}dx
limit as x approaches 0 of (3^x-10^x)/x	\lim\:_{x\to\:0}(\frac{3^{x}-10^{x}}{x})
integral from 0 to 1 of 7/(1+x^2)	\int\:_{0}^{1}\frac{7}{1+x^{2}}dx
integral of 2sin(1/2 x)	\int\:2\sin(\frac{1}{2}x)dx
derivative of 300x-10x^2+(x^3/3)	\frac{d}{dx}(300x-10x^{2}+\frac{x^{3}}{3})
integral from 0 to 1 of 8e^{-2x}	\int\:_{0}^{1}8e^{-2x}dx
limit as x approaches 8 of x-8	\lim\:_{x\to\:8}(x-8)
inverse oflaplace (10s-3)/(s^2+4s+29)	inverselaplace\:\frac{10s-3}{s^{2}+4s+29}
tangent of f(x)=sin(x),\at x=(5pi)/2	tangent\:f(x)=\sin(x),\at\:x=\frac{5π}{2}
derivative of 1/(3-x)	derivative\:\frac{1}{3-x}
integral from 1 to e of (x^2+x+1)/x	\int\:_{1}^{e}\frac{x^{2}+x+1}{x}dx
integral from-2 to 3 of (19)/(x^4)	\int\:_{-2}^{3}\frac{19}{x^{4}}dx
limit as x approaches 2 of-1/(x-2)	\lim\:_{x\to\:2}(-\frac{1}{x-2})
integral of (3-x^2)^3	\int\:(3-x^{2})^{3}dx
derivative of f(x)=e^{x^3}	derivative\:f(x)=e^{x^{3}}
limit as x approaches-5+of (-2)/(x^2-25)	\lim\:_{x\to\:-5+}(\frac{-2}{x^{2}-25})
d/(dt)(1/(1+t^2))	\frac{d}{dt}(\frac{1}{1+t^{2}})

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