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Popular Calculus Problems

derivative of (1+csc(x)/(1-csc(x)))	\frac{d}{dx}(\frac{1+\csc(x)}{1-\csc(x)})
integral of cos^2(4x)sin^3(4x)	\int\:\cos^{2}(4x)\sin^{3}(4x)dx
limit as x approaches infinity of 7^{2x}	\lim\:_{x\to\:\infty\:}(7^{2x})
tangent of x^4+4x^2-x	tangent\:x^{4}+4x^{2}-x
(d^2)/(dx^2)(sin(7x))	\frac{d^{2}}{dx^{2}}(\sin(7x))
integral from 1 to 2 of (x-1/x)^2	\int\:_{1}^{2}(x-\frac{1}{x})^{2}dx
(1-x^2)y^'-x^2y=(1+x)sqrt(1-x^2)	(1-x^{2})y^{\prime\:}-x^{2}y=(1+x)\sqrt{1-x^{2}}
integral of (x^3+sqrt(x))	\int\:(x^{3}+\sqrt{x})dx
derivative of arcsin(sqrt(2x))	\frac{d}{dx}(\arcsin(\sqrt{2x}))
(\partial)/(\partial x)(yln(x))	\frac{\partial\:}{\partial\:x}(y\ln(x))
integral of 12t^3	\int\:12t^{3}dt
(\partial)/(\partial x)(x^2y+xy^2+20)	\frac{\partial\:}{\partial\:x}(x^{2}y+xy^{2}+20)
derivative of x^{0.7}y^{0.3}	\frac{d}{dx}(x^{0.7}y^{0.3})
d/(dy)(3cos(3x)(x-y)+sin(3x))	\frac{d}{dy}(3\cos(3x)(x-y)+\sin(3x))
derivative of (4x^4+7/(x^2))	\frac{d}{dx}(\frac{4x^{4}+7}{x^{2}})
y^'=0.06y-0.0006y^2	y^{\prime\:}=0.06y-0.0006y^{2}
sum from n=1 to infinity of (n^3)/(n^3)	\sum\:_{n=1}^{\infty\:}\frac{n^{3}}{n^{3}}
derivative of 3x^3-2x^2-5x+2	\frac{d}{dx}(3x^{3}-2x^{2}-5x+2)
limit as x approaches 0 of xcsc(3x)	\lim\:_{x\to\:0}(x\csc(3x))
derivative of ln(4x^2+3x+3)	\frac{d}{dx}(\ln(4)x^{2}+3x+3)
integral of (6sin(x)+3sinh(x))	\int\:(6\sin(x)+3\sinh(x))dx
integral of (2x+1)/(x^2+1)	\int\:\frac{2x+1}{x^{2}+1}dx
integral of x/(sqrt(x^2+4x+8))	\int\:\frac{x}{\sqrt{x^{2}+4x+8}}dx
integral from-2 to 2 of \|x\|	\int\:_{-2}^{2}\left\|x\right\|dx
inverse oflaplace 6/(s(2s^2+7s+3))	inverselaplace\:\frac{6}{s(2s^{2}+7s+3)}
inverse oflaplace ((s^2-1))/((s^2+1)^2)	inverselaplace\:\frac{(s^{2}-1)}{(s^{2}+1)^{2}}
derivative of 3x^2e^x+e^x(x^3+3)	derivative\:3x^{2}e^{x}+e^{x}(x^{3}+3)
derivative of arctan(3x)	derivative\:\arctan(3x)
integral of cos^4(2θ)	\int\:\cos^{4}(2θ)dθ
derivative of e^{ax}cos(-bx)	\frac{d}{dx}(e^{ax}\cos(-bx))
integral from 1 to sqrt(3 of)x2^{(x^2)}	\int\:_{1}^{\sqrt{3}}x2^{(x^{2})}dx
derivative of (x^2-3x/(x-1))	\frac{d}{dx}(\frac{x^{2}-3x}{x-1})
limit as h approaches infinity of h^2-3h	\lim\:_{h\to\:\infty\:}(h^{2}-3h)
y^{''}+4y^'+6y=cos(x)	y^{\prime\:\prime\:}+4y^{\prime\:}+6y=\cos(x)
limit as x approaches 1/2 of 2x-1	\lim\:_{x\to\:\frac{1}{2}}(2x-1)
derivative of (5x+2/(sqrt(x+1)))	\frac{d}{dx}(\frac{5x+2}{\sqrt{x+1}})
inverse oflaplace 4/(s+4)	inverselaplace\:\frac{4}{s+4}
derivative of x-(x/2 ^2+(x/3)^3)	\frac{d}{dx}(x-(\frac{x}{2})^{2}+(\frac{x}{3})^{3})
derivative of ln(ln(5x))	derivative\:\ln(\ln(5x))
limit as x approaches infinity of (1+3/x)^{x/4}	\lim\:_{x\to\:\infty\:}((1+\frac{3}{x})^{\frac{x}{4}})
derivative of h(x)=ln(x+sqrt(x^2-7))	derivative\:h(x)=\ln(x+\sqrt{x^{2}-7})
inverse oflaplace (-2s+1)/(s^2+2s-8)	inverselaplace\:\frac{-2s+1}{s^{2}+2s-8}
limit as x approaches 0 of (x+4)/x	\lim\:_{x\to\:0}(\frac{x+4}{x})
integral of 3/((x+5)^2+4)	\int\:\frac{3}{(x+5)^{2}+4}dx
derivative of esin(x)	\frac{d}{dx}(e\sin(x))
derivative of (1/(y^2)-3/(y^4))(y+9y^3)	derivative\:(\frac{1}{y^{2}}-\frac{3}{y^{4}})(y+9y^{3})
limit as h approaches 0 of ((x+h)^2-9)/h	\lim\:_{h\to\:0}(\frac{(x+h)^{2}-9}{h})
area x^3,-x,1	area\:x^{3},-x,1
sum from n=0 to infinity of cos(1/n)	\sum\:_{n=0}^{\infty\:}\cos(\frac{1}{n})
limit as x approaches 0 of 4-ln(x)	\lim\:_{x\to\:0}(4-\ln(x))
integral of (5cos(x)-3sin(x))	\int\:(5\cos(x)-3\sin(x))dx
integral of x^2(2x^3+5)^4	\int\:x^{2}(2x^{3}+5)^{4}dx
integral of cos(6x)	\int\:\cos(6x)dx
integral of (x^5+1)e^{x^6+6x}	\int\:(x^{5}+1)e^{x^{6}+6x}dx
(\partial)/(\partial x)(x(x+1)^2)	\frac{\partial\:}{\partial\:x}(x(x+1)^{2})
sum from n=1 to infinity of 4/(n^2+5n+6)	\sum\:_{n=1}^{\infty\:}\frac{4}{n^{2}+5n+6}
integral of (sin(9/x))/(x^2)	\int\:\frac{\sin(\frac{9}{x})}{x^{2}}dx
(\partial)/(\partial x)(x^2-10x+y^2+8)	\frac{\partial\:}{\partial\:x}(x^{2}-10x+y^{2}+8)
inverse oflaplace 1/((s^3+4s))	inverselaplace\:\frac{1}{(s^{3}+4s)}
laplacetransform 10(t-1)	laplacetransform\:10(t-1)
(2x-5y+2)dx+(1-6y-5x)dy=0	(2x-5y+2)dx+(1-6y-5x)dy=0
(\partial)/(\partial x)((2x+3y)^7)	\frac{\partial\:}{\partial\:x}((2x+3y)^{7})
derivative of-16x^2+64x	\frac{d}{dx}(-16x^{2}+64x)
integral of (x^{-1/3})/(1+x^{1/6)}	\int\:\frac{x^{-\frac{1}{3}}}{1+x^{\frac{1}{6}}}dx
integral of (3x+5)/(x^2+2x+10)	\int\:\frac{3x+5}{x^{2}+2x+10}dx
integral of xen(x)	\int\:xen(x)dx
integral of (sqrt(x)+1/(7sqrt(x)))	\int\:(\sqrt{x}+\frac{1}{7\sqrt{x}})dx
derivative of 2x-2sqrt(x)	\frac{d}{dx}(2x-2\sqrt{x})
derivative of (2x^6+5x^3^{3/5})	\frac{d}{dx}((2x^{6}+5x^{3})^{\frac{3}{5}})
sum from n=1 to infinity of 1+(1/2)^n	\sum\:_{n=1}^{\infty\:}1+(\frac{1}{2})^{n}
x^2y^{''}-3xy^'+4y=x	x^{2}y^{\prime\:\prime\:}-3xy^{\prime\:}+4y=x
limit as x approaches-infinity of 7/x-2	\lim\:_{x\to\:-\infty\:}(\frac{7}{x}-2)
(\partial)/(\partial x)(0.5ln(x^2+y^2))	\frac{\partial\:}{\partial\:x}(0.5\ln(x^{2}+y^{2}))
derivative of y=5x^6ln(x)	derivative\:y=5x^{6}\ln(x)
limit as x approaches 0 of 1/(cos(x)-1)	\lim\:_{x\to\:0}(\frac{1}{\cos(x)-1})
derivative of sqrt(3)x^4	\frac{d}{dx}(\sqrt{3}x^{4})
limit as x approaches a of \sqrt[3]{27}	\lim\:_{x\to\:a}(\sqrt[3]{27})
integral of (8t-5)/(t+1)	\int\:\frac{8t-5}{t+1}dt
integral of 24x^3	\int\:24x^{3}dx
limit as x approaches 2 of (x-2)/(2-x)	\lim\:_{x\to\:2}(\frac{x-2}{2-x})
inverse oflaplace (4s)/(4s^2+1)	inverselaplace\:\frac{4s}{4s^{2}+1}
limit as x approaches 2 of arctan(x-2)	\lim\:_{x\to\:2}(\arctan(x-2))
derivative of 2/(t+1)	derivative\:\frac{2}{t+1}
derivative of 46-x/(250)	derivative\:46-\frac{x}{250}
derivative of (12)/(x^2(x-3))	derivative\:\frac{12}{x^{2}(x-3)}
derivative of e^{x^4}	derivative\:e^{x^{4}}
integral of (4x^3y^2-2xy^3)	\int\:(4x^{3}y^{2}-2xy^{3})dx
derivative of 5^{sin(3x})	\frac{d}{dx}(5^{\sin(3x)})
xln(x/y)dy-ydx=0	x\ln(\frac{x}{y})dy-ydx=0
derivative of (6x^2+2x+4/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+2x+4}{\sqrt{x}})
derivative of f(x)=6xe^x	derivative\:f(x)=6xe^{x}
derivative of (x^4-1(x^2+1))	\frac{d}{dx}((x^{4}-1)(x^{2}+1))
integral of (8x^5-8x^{-3})	\int\:(8x^{5}-8x^{-3})dx
derivative of e^{xy}	derivative\:e^{xy}
inverse oflaplace (10)/(s(s^2+10s+50))	inverselaplace\:\frac{10}{s(s^{2}+10s+50)}
limit as x approaches-4 of 6x+1	\lim\:_{x\to\:-4}(6x+1)
integral of (2x^2+x-1)/(x^3-2x^2+x)	\int\:\frac{2x^{2}+x-1}{x^{3}-2x^{2}+x}dx
integral of 1/(sqrt(x^2+4x+13))	\int\:\frac{1}{\sqrt{x^{2}+4x+13}}dx
y^{''}+9y=5sec(3t)	y^{\prime\:\prime\:}+9y=5\sec(3t)
derivative of ((x+1/(x-3))^2)	\frac{d}{dx}((\frac{x+1}{x-3})^{2})

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