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Popular Calculus Problems

integral of 1/(10-0.8x)	\int\:\frac{1}{10-0.8x}dx
y^{''}-10y^'+25y=4xe^{5x}	y^{\prime\:\prime\:}-10y^{\prime\:}+25y=4xe^{5x}
(\partial)/(\partial x)(9xe^{2xy})	\frac{\partial\:}{\partial\:x}(9xe^{2xy})
inverse oflaplace (s^2+2s+5)/(s^2(s+1))	inverselaplace\:\frac{s^{2}+2s+5}{s^{2}(s+1)}
maclaurin e^{iθ}	maclaurin\:e^{iθ}
d/(dz)(e^{iz})	\frac{d}{dz}(e^{iz})
(dy)/(dt)=1.7y	\frac{dy}{dt}=1.7y
derivative of f(x)=(x-5)(x+1)	derivative\:f(x)=(x-5)(x+1)
integral of 4e^{3x+e^{3x}}	\int\:4e^{3x+e^{3x}}dx
implicit (dy)/(dx),8x+3y=7	implicit\:\frac{dy}{dx},8x+3y=7
integral of tan^{1/2}(x)sec^4(x)	\int\:\tan^{\frac{1}{2}}(x)\sec^{4}(x)dx
derivative of 1/3 x^3+x^2	\frac{d}{dx}(\frac{1}{3}x^{3}+x^{2})
inverse oflaplace ((s+1))/(s^2+s+1/2)	inverselaplace\:\frac{(s+1)}{s^{2}+s+\frac{1}{2}}
integral of 6/((x-2)(x+4))	\int\:\frac{6}{(x-2)(x+4)}dx
(\partial)/(\partial x)((3x+4y)^5)	\frac{\partial\:}{\partial\:x}((3x+4y)^{5})
derivative of y=(x^5)/(1-x^4)	derivative\:y=\frac{x^{5}}{1-x^{4}}
limit as x approaches infinity of sin(0)	\lim\:_{x\to\:\infty\:}(\sin(0))
sum from n=2 to infinity of (ln(n))/(7n)	\sum\:_{n=2}^{\infty\:}\frac{\ln(n)}{7n}
sum from n=0 to infinity of (2n)/(n^2+1)	\sum\:_{n=0}^{\infty\:}\frac{2n}{n^{2}+1}
derivative of x/(x^2+4)	derivative\:\frac{x}{x^{2}+4}
derivative of sqrt(x\sqrt{x^2+1)}	derivative\:\sqrt{x\sqrt{x^{2}+1}}
derivative of (sqrt(x^2+1)/x)	\frac{d}{dx}(\frac{\sqrt{x^{2}+1}}{x})
derivative of 1/(x^3+2)	\frac{d}{dx}(\frac{1}{x^{3}+2})
limit as x approaches 2 of x^3-2x^2+x-3	\lim\:_{x\to\:2}(x^{3}-2x^{2}+x-3)
derivative of (2-3x^2)^4(x^7+3)^3	derivative\:(2-3x^{2})^{4}(x^{7}+3)^{3}
derivative of f(x)=(sqrt(x))/4	derivative\:f(x)=\frac{\sqrt{x}}{4}
derivative of 2+sqrt(5x)	\frac{d}{dx}(2+\sqrt{5x})
sum from n=2 to infinity of n^2-n	\sum\:_{n=2}^{\infty\:}n^{2}-n
d/(dz)((z^2)/2-(z^7)/7)	\frac{d}{dz}(\frac{z^{2}}{2}-\frac{z^{7}}{7})
derivative of sqrt(x)cos(x)	\frac{d}{dx}(\sqrt{x}\cos(x))
integral of cos^7(x)tan^3(x)	\int\:\cos^{7}(x)\tan^{3}(x)dx
derivative of x^{sqrt(5)}	\frac{d}{dx}(x^{\sqrt{5}})
integral of (8x)/(sqrt(1-x^4))	\int\:\frac{8x}{\sqrt{1-x^{4}}}dx
integral of (cos^7(x))sin(x)	\int\:(\cos^{7}(x))\sin(x)dx
derivative of cos^2(x-sin^2(x))	\frac{d}{dx}(\cos^{2}(x)-\sin^{2}(x))
y^'+y/x =2x^4y^2	y^{\prime\:}+\frac{y}{x}=2x^{4}y^{2}
integral of e^{3x-8}	\int\:e^{3x-8}dx
derivative of e^{cos(4x})	\frac{d}{dx}(e^{\cos(4x)})
slope of (6.3)(7.8)	slope\:(6.3)(7.8)
tangent of 33x^3	tangent\:33x^{3}
integral of (a+bx^7)/(sqrt(8ax+bx^8))	\int\:\frac{a+bx^{7}}{\sqrt{8ax+bx^{8}}}dx
tangent of f(x)=4e^x+x,\at x=0	tangent\:f(x)=4e^{x}+x,\at\:x=0
derivative of cos((1-e^{7x}/(1+e^{7x)}))	\frac{d}{dx}(\cos(\frac{1-e^{7x}}{1+e^{7x}}))
f(x)=(csc(x))/(1+csc(x))	f(x)=\frac{\csc(x)}{1+\csc(x)}
derivative of f(x)=x^2*e^x	derivative\:f(x)=x^{2}\cdot\:e^{x}
integral from 1 to 4 of 4x^2	\int\:_{1}^{4}4x^{2}dx
integral of e^{sin(x)}	\int\:e^{\sin(x)}dx
derivative of 5xe^{-x}-3e^{x^2}	derivative\:5xe^{-x}-3e^{x^{2}}
limit as x approaches infinity of 10^x	\lim\:_{x\to\:\infty\:}(10^{x})
derivative of (6x)^{5x}	derivative\:(6x)^{5x}
d/(dy)(-x^2y^2sin(x)+2xy^2cos(x))	\frac{d}{dy}(-x^{2}y^{2}\sin(x)+2xy^{2}\cos(x))
integral of sqrt(x/(1-x))	\int\:\sqrt{\frac{x}{1-x}}dx
y^'=3-y	y^{\prime\:}=3-y
integral of (7x^3-3x^2+21x+6)/(x^3+3x)	\int\:\frac{7x^{3}-3x^{2}+21x+6}{x^{3}+3x}dx
(dy)/(dx)+3x^2y=sin(x)e^{-x^3}	\frac{dy}{dx}+3x^{2}y=\sin(x)e^{-x^{3}}
derivative of cos(sqrt(sin(tan(2pix))))	\frac{d}{dx}(\cos(\sqrt{\sin(\tan(2πx))}))
implicit cos(xy)=1+sin(y)	implicit\:\cos(xy)=1+\sin(y)
derivative of 4e^{3x^2}	\frac{d}{dx}(4e^{3x^{2}})
derivative of (2x^3+5)/(4x^2+7)	derivative\:\frac{2x^{3}+5}{4x^{2}+7}
taylor 1+x^2	taylor\:1+x^{2}
derivative of-1/4 (x^{-4}-x^8)	derivative\:-\frac{1}{4}(x^{-4}-x^{8})
laplacetransform e^{-pi/2 t}	laplacetransform\:e^{-\frac{π}{2}t}
integral of e^{1/2 x^2}*x^3	\int\:e^{\frac{1}{2}x^{2}}\cdot\:x^{3}dx
derivative of (4+x^2^{-1})	\frac{d}{dx}((4+x^{2})^{-1})
integral of (x^8-(2x^5)/7-sqrt(5))	\int\:(x^{8}-\frac{2x^{5}}{7}-\sqrt{5})dx
y^'=(x^2+xy+y^2)/(x^2)	y^{\prime\:}=\frac{x^{2}+xy+y^{2}}{x^{2}}
dy=(x-2xy)dx	dy=(x-2xy)dx
tangent of x^2+4x-8	tangent\:x^{2}+4x-8
limit as x approaches 0+of x^5ln(x)	\lim\:_{x\to\:0+}(x^{5}\ln(x))
limit as x approaches 1-of 6x-2	\lim\:_{x\to\:1-}(6x-2)
(\partial)/(\partial x)(3x^2y^2+x/y)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{2}+\frac{x}{y})
derivative of y=sin(3x+2y)	derivative\:y=\sin(3x+2y)
integral of (5-3x+x^2)	\int\:(5-3x+x^{2})dx
derivative of 1/(5-x)	\frac{d}{dx}(\frac{1}{5-x})
tangent of f(x)=e^{-2x},(0,1)	tangent\:f(x)=e^{-2x},(0,1)
y^{''}-2y^'+10y=e^{-x}	y^{\prime\:\prime\:}-2y^{\prime\:}+10y=e^{-x}
derivative of e^{-x+1}-e^{-x+1}*x	derivative\:e^{-x+1}-e^{-x+1}\cdot\:x
(\partial)/(\partial x)(y*cos(x-y))	\frac{\partial\:}{\partial\:x}(y\cdot\:\cos(x-y))
tangent of 7x-4x^2	tangent\:7x-4x^{2}
integral of-1/(2\sqrt[3]{x^2)}	\int\:-\frac{1}{2\sqrt[3]{x^{2}}}dx
integral of 11ln(\sqrt[3]{x})	\int\:11\ln(\sqrt[3]{x})dx
y^'=y(4-ty)	y^{\prime\:}=y(4-ty)
derivative of cos^2(x+sin^2(x))	\frac{d}{dx}(\cos^{2}(x)+\sin^{2}(x))
integral of x^2cos(8x)	\int\:x^{2}\cos(8x)dx
derivative of f(x)=(56)/(x^9)	derivative\:f(x)=\frac{56}{x^{9}}
limit as x approaches 0 of x^2-3	\lim\:_{x\to\:0}(x^{2}-3)
limit as x approaches 2 of (x+5)/(x-2)	\lim\:_{x\to\:2}(\frac{x+5}{x-2})
integral of 2sin(x)-1	\int\:2\sin(x)-1dx
derivative of sin^5(sqrt(ln(e^{3x-1)}))	\frac{d}{dx}(\sin^{5}(\sqrt{\ln(e^{3x-1})}))
integral of te^{-t}-2	\int\:te^{-t}-2dt
integral of 2sqrt(x)+6cos(x)	\int\:2\sqrt{x}+6\cos(x)dx
integral of (25-x^2)^{1/2}	\int\:(25-x^{2})^{\frac{1}{2}}dx
derivative of 1/(e^x-1)	\frac{d}{dx}(\frac{1}{e^{x}-1})
derivative of e^{3x}(-2sin(2x)+3cos(2x))	derivative\:e^{3x}(-2\sin(2x)+3\cos(2x))
integral of x^5+2x^3+x	\int\:x^{5}+2x^{3}+xdx
derivative of x+60	\frac{d}{dx}(x+60)
integral from 0 to infinity of 1/(x^5)	\int\:_{0}^{\infty\:}\frac{1}{x^{5}}dx
integral of ye^{x/y}	\int\:ye^{\frac{x}{y}}dx
integral of x/(sqrt(12-9x^2))	\int\:\frac{x}{\sqrt{12-9x^{2}}}dx
integral from 1 to 4 of sqrt(x)(2+x)	\int\:_{1}^{4}\sqrt{x}(2+x)dx

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