Topic
Q:
Evaluate the integral of the product of two functions:
\[ \int\left(2 x^{2} \cdot e^{x}\right) d x \]
Q:
Consider the indefinite integral \( \int x \cdot \sqrt[2]{x^{2}+6} d x \) :
This can be transformed into a basic integral by letting
\( u=\square \) and
\( d u=\square \)
Q:
Evaluate the integral of the product of two functions:
\[ \int\left(2 x^{2} \cdot e^{x}\right) d x \]
Q:
Evaluate the integral
by making the appropriate substitution: \( u=\square \frac{d x}{(2 x+2)^{4}} \),
\( \int \frac{d x}{(2 x+2)^{4}}=\square \)
Q:
Evaluate the indefinite integral.
\( \int \frac{5}{(t+3)^{2}} d t \)
\( \square+C \)
Q:
Given two sequences \( \left\{a_{n}\right\} \) and \( \left\{b_{n}\right\} \) :
\[ \begin{aligned} a_{n} & =\frac{2 n}{n+1} \\ b_{n} & =\frac{1}{n^{2}}\end{aligned} \]
Q:
Evaluate the indefinite integral.
\( \int x^{2} \sqrt{15+x^{3}} d x \)
\( \square+C \)
Q:
Evaluate the definite integral.
\( \int_{0}^{\frac{\pi}{4}} \sin (4 t) d t \)
Q:
Evaluate the indefinite integral
\( \int 5 \sin ^{4} x \cos x d x= \)
Q:
Evaluate the definite integral.
\( \int_{0}^{1} \sqrt{1 x+3} d x \)
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