Evaluate
\frac{2t^{2}x^{6}}{3}+С
Differentiate w.r.t. x
4t^{2}x^{5}
শেয়ার করুন
ক্লিপবোর্ডে কপি করা হয়েছে
\int x\times 2^{2}t^{2}\left(x^{2}\right)^{2}\mathrm{d}x
Expand \left(2tx^{2}\right)^{2}.
\int x\times 2^{2}t^{2}x^{4}\mathrm{d}x
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
\int x\times 4t^{2}x^{4}\mathrm{d}x
Calculate 2 to the power of 2 and get 4.
\int x^{5}\times 4t^{2}\mathrm{d}x
To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.
4t^{2}\int x^{5}\mathrm{d}x
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
4t^{2}\times \frac{x^{6}}{6}
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{5}\mathrm{d}x with \frac{x^{6}}{6}.
\frac{2t^{2}x^{6}}{3}
Simplify.
\frac{2t^{2}x^{6}}{3}+С
If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
উদাহরণ
দ্বিঘাত সমীকরণ
{ x } ^ { 2 } - 4 x - 5 = 0
ত্রিকোণমিতি
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রৈখিক সমীকরণ
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পাটিগণিত
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মেট্রিক্স
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
সমকালীন সমীকরণ
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ডিফারেন্সিয়েশন
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ইন্টিগ্রেশন
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লিমিট
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