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Popular Calculus Problems

integral from 0 to 1 of x^2(x+1)^7	\int\:_{0}^{1}x^{2}(x+1)^{7}dx
(\partial)/(\partial y)(2xy^3-4)	\frac{\partial\:}{\partial\:y}(2xy^{3}-4)
y^{''}-18y^'+81y=0	y^{\prime\:\prime\:}-18y^{\prime\:}+81y=0
integral of 16tan^3(x)	\int\:16\tan^{3}(x)dx
derivative of g(w)=10sqrt(w)	derivative\:g(w)=10\sqrt{w}
(\partial)/(\partial x)(x^4y)	\frac{\partial\:}{\partial\:x}(x^{4}y)
integral of t*sin(2t)	\int\:t\cdot\:\sin(2t)dt
derivative of (8(5x)^4+5)^3	derivative\:(8(5x)^{4}+5)^{3}
derivative of 1/(x^4-3/(x^2)+x^3)	\frac{d}{dx}(\frac{1}{x^{4}}-\frac{3}{x^{2}}+x^{3})
integral of 1/(2x^2+3)	\int\:\frac{1}{2x^{2}+3}dx
tangent of f(x)=x^2-6x+9,(-2,25)	tangent\:f(x)=x^{2}-6x+9,(-2,25)
limit as v approaches 3 of (sqrt(v+1)-2)/(v-3)	\lim\:_{v\to\:3}(\frac{\sqrt{v+1}-2}{v-3})
limit as x approaches 3 of (x-2)/(x^2-9)	\lim\:_{x\to\:3}(\frac{x-2}{x^{2}-9})
integral of 1/(x^2+4x+5)	\int\:\frac{1}{x^{2}+4x+5}dx
tangent of f(x)= 9/(x-3),\at x=2	tangent\:f(x)=\frac{9}{x-3},\at\:x=2
derivative of y=e^5	derivative\:y=e^{5}
derivative of x^{3/4}-3x^{1/4}	\frac{d}{dx}(x^{\frac{3}{4}}-3x^{\frac{1}{4}})
derivative of (3.3x+5)^{0.37}	derivative\:(3.3x+5)^{0.37}
derivative of 1/(2x^{5/2})	\frac{d}{dx}(\frac{1}{2x^{\frac{5}{2}}})
y^'=(y+9x)^2	y^{\prime\:}=(y+9x)^{2}
inverse oflaplace ((e^{-2s}))/s	inverselaplace\:\frac{(e^{-2s})}{s}
integral of-2x^5-5x^3+3x^2+1-4e^x	\int\:-2x^{5}-5x^{3}+3x^{2}+1-4e^{x}dx
integral from 2 to 3 of 2/(t^2-1)	\int\:_{2}^{3}\frac{2}{t^{2}-1}dt
integral of 5/(xsqrt(x^2+9))	\int\:\frac{5}{x\sqrt{x^{2}+9}}dx
derivative of \sqrt[3]{t^2}-4sqrt(t^3)	derivative\:\sqrt[3]{t^{2}}-4\sqrt{t^{3}}
derivative of sqrt(x)	derivative\:\sqrt{x}
derivative of xln(x^{18})	\frac{d}{dx}(x\ln(x^{18}))
integral of (x^2+3x-1)/(x+2)	\int\:\frac{x^{2}+3x-1}{x+2}dx
integral from 0 to 3 of (8-2x)	\int\:_{0}^{3}(8-2x)dx
(\partial)/(\partial y)(sin(xy)+xsin(y))	\frac{\partial\:}{\partial\:y}(\sin(xy)+x\sin(y))
f(x)= 6/(x^4)	f(x)=\frac{6}{x^{4}}
integral of e^{-3/2 x}	\int\:e^{-\frac{3}{2}x}dx
derivative of 6x^3-9x^2+5x-2	derivative\:6x^{3}-9x^{2}+5x-2
area 7cos(pix),8x^2-2,[-0.5,0.5]	area\:7\cos(πx),8x^{2}-2,[-0.5,0.5]
limit as x approaches-1 of (3x^2-9x-12)/(3x+3)	\lim\:_{x\to\:-1}(\frac{3x^{2}-9x-12}{3x+3})
integral of (6+x)/(sqrt(36-x^2))	\int\:\frac{6+x}{\sqrt{36-x^{2}}}dx
implicit (dy)/(dx),7xy+1=0	implicit\:\frac{dy}{dx},7xy+1=0
derivative of 9^xln(x)	\frac{d}{dx}(9^{x}\ln(x))
laplacetransform 5t^2-6cos(3t)+8e^{-t}	laplacetransform\:5t^{2}-6\cos(3t)+8e^{-t}
limit as x approaches infinity of x+2/x	\lim\:_{x\to\:\infty\:}(x+\frac{2}{x})
limit as x approaches 4 of 5x	\lim\:_{x\to\:4}(5x)
derivative of (sqrt(s)-1)/(sqrt(s)+3)	derivative\:\frac{\sqrt{s}-1}{\sqrt{s}+3}
derivative of (y^3/(x^2))	\frac{d}{dx}(\frac{y^{3}}{x^{2}})
(\partial)/(\partial y)(x^5y)	\frac{\partial\:}{\partial\:y}(x^{5}y)
integral of cos(2t)e^{-st}	\int\:\cos(2t)e^{-st}dt
derivative of ({f}(x)/(x^4))	\frac{d}{dx}(\frac{{f}(x)}{x^{4}})
(\partial)/(\partial x)(2x-3cos(x)+10y)	\frac{\partial\:}{\partial\:x}(2x-3\cos(x)+10y)
derivative of 8/x-2/(x^3+1/(x^4))	\frac{d}{dx}(\frac{8}{x}-\frac{2}{x^{3}}+\frac{1}{x^{4}})
x^2y^{''}+4xy^'+2y=0	x^{2}y^{\prime\:\prime\:}+4xy^{\prime\:}+2y=0
limit as x approaches 8 of x+8	\lim\:_{x\to\:8}(x+8)
limit as x approaches infinity of ln(2)	\lim\:_{x\to\:\infty\:}(\ln(2))
inverse oflaplace ((3s-17))/(s^2-2s-3)	inverselaplace\:\frac{(3s-17)}{s^{2}-2s-3}
sum from n=0 to infinity of (2/e)^n	\sum\:_{n=0}^{\infty\:}(\frac{2}{e})^{n}
expand (x^2+4)^5	expand\:(x^{2}+4)^{5}
integral of (e^{2x})	\int\:(e^{2x})dx
derivative of x^x	derivative\:x^{x}
derivative of 1/(sqrt(10x+11))	\frac{d}{dx}(\frac{1}{\sqrt{10x+11}})
integral from-infinity to 0 of 1/(x^2+1)	\int\:_{-\infty\:}^{0}\frac{1}{x^{2}+1}dx
(\partial)/(\partial y)(4arctan(x/y))	\frac{\partial\:}{\partial\:y}(4\arctan(\frac{x}{y}))
integral of 3x^2cos(3x)	\int\:3x^{2}\cos(3x)dx
derivative of f(x)=ln(256sin^2(x))	derivative\:f(x)=\ln(256\sin^{2}(x))
laplacetransform t*1	laplacetransform\:t\cdot\:1
integral of 1/18 x^2	\int\:\frac{1}{18}x^{2}dx
integral from 0 to 4 of pi(x^2-4x)^2	\int\:_{0}^{4}π(x^{2}-4x)^{2}dx
integral of 5^{cos(x)}sin(x)	\int\:5^{\cos(x)}\sin(x)dx
d/(dy)(2x^3+6xy^2-3x^2+3y^2)	\frac{d}{dy}(2x^{3}+6xy^{2}-3x^{2}+3y^{2})
(dy)/(dx)=(1+2y)/(1+x)	\frac{dy}{dx}=\frac{1+2y}{1+x}
laplacetransform 1+2t	laplacetransform\:1+2t
(d^2)/(dx^2)(1/(1+x^2))	\frac{d^{2}}{dx^{2}}(\frac{1}{1+x^{2}})
integral of (3x-4/3 x^{3/2})	\int\:(3x-\frac{4}{3}x^{\frac{3}{2}})dx
limit as x approaches 1-of arcsin(1/x)	\lim\:_{x\to\:1-}(\arcsin(\frac{1}{x}))
derivative of t^3-15t^2+72t	derivative\:t^{3}-15t^{2}+72t
derivative of e^{-ax}cos(bx)	\frac{d}{dx}(e^{-ax}\cos(bx))
area y=\|x\|,y=x^2	area\:y=\left\|x\right\|,y=x^{2}
integral of (sin(θ)-1)/(cos^2(θ))	\int\:\frac{\sin(θ)-1}{\cos^{2}(θ)}dθ
(\partial)/(\partial y)(e^{-xy})	\frac{\partial\:}{\partial\:y}(e^{-xy})
(\partial)/(\partial x)(ye^{x/y}-z)	\frac{\partial\:}{\partial\:x}(ye^{\frac{x}{y}}-z)
derivative of (x^2/(5+8x))	\frac{d}{dx}(\frac{x^{2}}{5+8x})
integral of 1/((x-5)(x-3))	\int\:\frac{1}{(x-5)(x-3)}dx
laplacetransform 3e^{-3t}	laplacetransform\:3e^{-3t}
derivative of sin^2(x+1)	\frac{d}{dx}(\sin^{2}(x)+1)
limit as x approaches 0-of (8x^4-3x)/x	\lim\:_{x\to\:0-}(\frac{8x^{4}-3x}{x})
limit as x approaches 0 of 2x-2	\lim\:_{x\to\:0}(2x-2)
integral from 0 to 1 of x^3sqrt(1-x)	\int\:_{0}^{1}x^{3}\sqrt{1-x}dx
derivative of (2x/((3y^2)))	\frac{d}{dx}(\frac{2x}{(3y^{2})})
integral from 0 to L of (3ax^2+2bx+c)^2	\int\:_{0}^{L}(3ax^{2}+2bx+c)^{2}dx
integral of e^{1-x}	\int\:e^{1-x}dx
integral of 8x+5	\int\:8x+5dx
derivative of {z}(x)	\frac{d}{dx}({z}(x))
integral of (1/(5-t)+60e^{-0.3t}+t)	\int\:(\frac{1}{5-t}+60e^{-0.3t}+t)dt
integral of 3xln(5x)	\int\:3x\ln(5x)dx
integral of (14)/(sec(2x)-1)	\int\:\frac{14}{\sec(2x)-1}dx
derivative of f(x)=5x^4+8sin(x)	derivative\:f(x)=5x^{4}+8\sin(x)
(-e^{-x})^'	(-e^{-x})^{\prime\:}
inverse oflaplace s/(s^2+4)	inverselaplace\:\frac{s}{s^{2}+4}
integral of 5/(sqrt(1+x^2))	\int\:\frac{5}{\sqrt{1+x^{2}}}dx
integral of 4xe^{8x}	\int\:4xe^{8x}dx
y^{''}+6y^'+5y=0	y^{\prime\:\prime\:}+6y^{\prime\:}+5y=0
limit as x approaches 0 of x^{sqrt(x)}	\lim\:_{x\to\:0}(x^{\sqrt{x}})
derivative of 1/2 x^2sqrt(16-x^2)	derivative\:\frac{1}{2}x^{2}\sqrt{16-x^{2}}

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